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Slope Intercept Form Calculator

Slope Intercept Form Calculator

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Y₁

X₂

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The slope intercept form calculator helps you to find the equation of a line from given two points, one point & slope, and slope & intercept of a line. In the simplest term, this slope intercept calculator will determine the x and y-intercept as well as the slope of a line by using slope intercept equation.

Also, consider this simple slope calculator that finds a slope of a line passing through the two given points in the Cartesian coordinate plane.

Slope-Intercept Formula (Equation)

The slope intercept equation is mentioned below and an online lope intercept form equation calculator also uses the same equation to provides you the precise calculations for slope-intercept form.

y = mx+c

Slope-intercept form examples:

y=5x-9

y=-2x-7

y=3+5x

These all equations are in the slope-intercept form.

But:

7x+9y=1

8y-6=9(3x-7)

These equations are not in the slope-intercept form.

Also, this simple, but accurate point slope calculator helps to determine the equation of a line “y – y1 = m(x – x1)” by using the coordinate points and slope of the line.

The coefficients in slope-intercept form:

The great advantage of slope-intercept form is that it gives the two main features of a line.

  • The slope of a line (m).
  • The y-intercept of line or the line’s y-intercept at (0, c).

For example:

A line y=2x+1 having slope 2 and intercept c is 1.

Note:

This form gives the slope and y-intercept form of the line, that’s why it is called the slope-intercept form. Our slope intercept form calculator minimizes your worry by giving both coefficients of a line that are slope and y-intercept.

How to find c in slope-intercept form of a line?

As we know, the value of the x coordinate at y-axis is zero. So, if we have to find the y-intercept of the line then, we should substitute x=0 in the linear equation.

Example:

8y=9x+13

Substitute x=0 in this equation.

8y=9(0) + 13

8y=0+13

8y=13

y=13/8

This online y intercept finder displays the y-intercept of the line accurately so that you can come to know at which point the line intersects the y-axis.

Why (m) gives the slope of a line?

As we know about slope “ratio of the change in y to the change in x coordinates between any points of the line”:

m = change in y/change in x

m = Δy/Δx

m = rise/run

If a change in x is only one (1) unit, then the change in y equals the slope of the line,

m = change in y/1

m = change in y

Now, look at how much increases in y value by changing x values.

y=4x+9

                   x                                   y
0 1+0×4 = 1
1 1+1×4 = 1+4
2 1+2×4 = 1+4+4
3 1+3×4 = 1+4+4+4
4 1+4×4 = 1+4+4+4+4
5 1+5×4 = 1+4+4+4+4+4

 

We see that every time when x increases 1 unit, y increases 4 units. So, the slope of a line y=4x+9 is 4. Also, you can use slope and y intercept calculator that helps to find the slope-intercept form from the given slope (m) and y-intercept (c).

How to find the x-intercept of the line:

The value at which the straight line intersects the x-axis (horizontal axis). You can calculate the x-intercept in the following way:

y=mx+c

(0)=mx+c

-c=mx

-c/m=x

x=-c/m

Example:

Find the x-intercept of 9y=3x+7?

Solution:

You can find x-intercept of the given equation by using a basic slope intercept formula.

Substitute y=0 in the given equation (problem):

9(0) =3x+7

0=3x+7

-7=3x

x= -7/3

Our x and y intercept calculator helps you to find out the x and y-intercepts of a line for you.

Solving a Real-World problem with slope-intercept form:

It is helpful in many fields like in science linear models can be described in slope intercept form. In Statistics, the regression line can be found with the help of slope intercept form. Let’s solve a real-world problem with the slope-intercept form.

Example:

A boy is eating a 13.9cm long ice cream cone. It starts melting at a rate of 3cm/minute. If the boy didn’t eat the ice cream, how much left ice cream after 4 minutes?

Solution:

First of all,

Slope is -3 because ice cream is decreasing.

Y-intercept is 13.9 and x intercept is 4miutes.

Then, put the values in slope intercept form.

y=mx+c

y= (-3) (4) +13.9

y=-12+13.9

y=1.9

So, after 4minutes ice cream measures only 1.9cm.

It is difficult and tricky to do the complex calculations by hand; you can simply use above slope intercept form calculator..

Solving a real world problem uses x&y-intercepts:

The x and y intercepts of the line can be helpful in many of the real world problems. Consider a situation when a bike is moving towards you, its movement plotted in distance-time graph. The x-axis represents the time and y-axis represents the distance covered by the bike. Then, you can easily find out the time or distance at any point in the graph with the help of x&y intercepts.

Equations having no intercept:

We can differentiate the following three groups of linear equation:

  • An equation having only y-intercept.
  • An equation having only x-intercept.
  • An equation having neither x nor y-intercept.

The first two can be determined by this slope-intercept form calculator but the last type is not determined by the slope-intercept calculator. The last method is very tricky and to understand this type we need to know about the asymptotes.

Asymptote:

It is the line to which the function or curve comes closer or closer but never crosses or touches the line. Let’s talk about an example to clear the concept about asymptotes.

If we have an equation y=6/x and want to find the y intercept by substituting the value of x with 0, then we get the undefined answer.

The value of y increases very rapidly if we take the value closer to 0.In this scenario, a linear equation x=0 is the asymptote of the function y=6/x.

Graphing lines with integer slopes:

As the slope intercept form is y=mx+c , the slope is m and y-intercept is c. Therefore the slope of y=7x+2 is 7 and y-intercept is (0, 2).

For the graph of line, we need two points one point we already have is (0, 2).As the slope of line is 7 so, the other point is (0+1, 2+7) = (1, 9).

Now, the graph off this equation is as follow:

graphing lines with integer slopes

 

How to find slope intercept form With Calculator:

This slope intercept form calculator is 100% free that solve your slope-intercept form related-problems accurately. Now, just follow these steps to get instant outcomes!

Inputs:

You have three options to do calculations including:

  • Two points
  • One point and slope (m)
  • Intercept (c) & slope (m)

Well, come to the point:

  • First of all, you have to choose the one of the given options
  • Very next, you need to enter the remaining missing values into the designated fields according to the selected options
  • Once done, the time comes to hit the calculate button

Output:

The calculator helps to find:

  • Slope-Intercept form.
  • Slope of a line.
  • X & Y intercepts of the line.
  • Percentage Grade.
  • The angle of a line with x-axis.
  • Change in x (Δx) and change in y (Δy).
  • Distance between two points.

Note:

The output of the each option is different, the slope-intercept calculator display the results according to the selected option.

How to find slope-intercept form from two points (Step-By-Step)?

To find the slope intercept form from the given two points, just follow the given steps for manual calculation.

  • First of all, calculate the slope of a line with two points given.
  • Then, y-intercept of a line by enters the value of x, y & slope m in the slope equation.

Let’s have an example to clarify the concept:

For Example:

Find the slope intercept form of the points (2, -1) & (5, 3)?

Solution:

Step1:

Calculate the slope from two points with formula:

m = y2 – y1 /x2 – x1

Here,

y2 = 3

y1 = -1

x2 = 5

x1 = 2

m = 3 + 1 /5 – 2

m = 4 /3

m = 1.333

Step2:

Find out the y-intercept by entering the values of slope, y and x in equation.

3 = (1.333) (5) +c

3 = 6.665+c

c = 3-6.665

c = -3.665

Step3:

Now enter the values of slope and y-intercept to get the slope-intercept form.

y = 1.333x-3.665

How to find slope-intercept form from intercept (c) & slope (Step-By-Step):

To find the slope intercept form from the given intercept (c) & slope (m), just enter the values in the equation. Have a look at example:

Example:

Find out the slope-intercept form having slope -8 & y-intercept is 13?

Solution:

The equation is,

y = mx + c

y = (-8) x + 13

y = -8x + 13

Our free online calculator enables you to find the slope-intercept form equation from intercept (c) & slope (m) accurately.

Frequently Ask Questions (FAQ’s):

How do I write an equation for the line with a slope of 6 and y-intercept of -3?

You can write an equation for the line with slope and intercept given by using the formula:
y = mx + c
Here, m is 6 & c is -3.So,
y = 6x + -3

What is intercept and how do I calculate this using a graph?

As we know, there are two types of intercept, x & y-intercept. If the graph cuts the x-axis with coordinates (x, 0), then we say it is x-intercept. If the graph cuts the y-axis with coordinates (0,y) , then we say it is y-intercept. To find the x & y-intercept using a graph, just see where the line cuts the x & y-axis respectively.

If point (-2,-4) has a slope of 4, what is the equation?

You can find the equation of line with one point and slope with the formula:
y + 4 = 4 (x+2)
y + 4 = 4x+8
y = 4x+8-4
y = 4x+4

What is the slope of a line that has a y intercept of 5 and an x intercept of -5?

With these two points (0, 5) & (-5, 0), you can find the slope by the following formula.
m = 0 – 5 /-5 – 0
m = -5 /-5
m = 1

How do I find the y-intercept of the equation 2(x-1) ^2 + 5?

To find the y-intercept, put x=0 in the equation:
=2(0-1) ^2 + 5
=2(-1) ^2 + 5
= (-2) ^2 + 5
=4 + 5
=9

Can the y = mx + b formula be reversed to solve for x? If so, how?

Yes, the formula y = mx + b can be reversed to solve for x. It is possible if we subtract b from both sides and divide by m on both sides,
y – b = mx + b – b
y – b = mx
(y – b)/m = mx/m
(y – b)/m = x

If I have (3, -12) as my points and an x-intercept of one, what would the y-intercept be?

Using the two point method use above in the article, one point is (3,-12) & other is (1, 0). Find the slope of a line with the formula m = y2 – y1 /x2 – x1 line then, solve for the slope intercept form as y = mx+c.

After this substitute x=0 in the equation to find the y-intercept.

How do I find the y-intercept if the only given information is the slope and no graph or point(s) specified?

You can’t find the y-intercept with just slope given; you have to be given more information than the slope of a line.

What if the slope is undefined?

If the slope of a line is undefined means it is infinite, then the line is parallel to y-axis (vertical line).

What is the x-intercept of the equation 2x-y=8?

To find the x-intercept of the equation, set all the other variable set to zero.
2x – y = 8
2x – 0 = 8
2x = 8
2x/2 = 8/2
x = 4

End-Note:

The slope intercept form is very helpful in solving the real world problems, distance between the two points and slope of a line. Students use the slope-intercept form to better understand the different equations of line and how to determine the general equation of line. So, students and professional can use this online slope intercept form calculator to calculate the slope intercept form in a fraction of seconds.

References:

From the source of khanacademy: Intro to slope-intercept form (Explore Now)

From the source of ixl (learning): Slope-intercept form: write an equation from a graph

From the source of ck12: Slope-Intercept Form of Linear Equations (Explore equations in y = mx+b form)