Standard Form to Slope Intercept Form Calculator

Standard Form to Slope Intercept Form Calculator

Select and put the values accordingly into the calculator to find standard form and slope form of an equation.

To Calculate:

Standard Form: Ax + By + C = 0

Enter A

Enter B

Enter C

Standard Form to Slope Intercept Form Calculator

The standard form to slope intercept form calculator allows you to determine both standard form and slope form of an equation. You can convert linear equations between their Slope-Intercept Form and Standard Form. So select type of conversion from drop-down menu to convert linear equations between the two forms.

Standard Form of An Equation:

The generic form of a linear equation is written in the format given below:

A{x} + B{y} = C

Where:

A and B and C are the coefficients
x and y are the respective variables involved

You can convert intercept form to its corresponding standard form by using slope to standard form calculator.

Slope Intercept Form of An Equation:

You can write the equation in its intercept form as follows:

y = mx + c

You can also find the slope intercept form of an equation by using our slope intercept form calculator.

How To Convert Standard From To Slope Intercept Form?

In this section, we will be solving a couple of examples for you so that you may not feel any difficulty while doing calculations.

Example # 01:

Convert the following standard form of the equation into its respective slope intercept form

2x - 9y = 15

Solution:

As we know that the slope intercept form of the equation is as follows:

y = mx + c

Converting the given equation in its slope intercept form now:

2x - 9y = 15

-9y = -2x + 15

-9y = -(2x + 15)

9y = 2x - 15

y = 2x - 15 9

y = 2x 9 - 15 9

y = 0.222x -1.666

Which is the required slope intercept form of the given standard equation. Now we have:

Slope = 0.222

For x-intercept, we have:

y = mx +c

Putting y = 0:

0 = mx + c

x = - c m

x = - 1.666 0.222

x = 7.5

Y-intercept = -1.666

Percentage Grade = Slope * 100

Percentage Grade = 0.222 * 100

Percentage Grade = 22.22%

For angle, we have:

θ = arctan y x

θ = arctan −1.666 7.5

θ = arctan(0.222)

θ = 12.51ᵒ

Example # 02:

Convert the following slope intercept form of the equation into its standard form:

y = 1 9 x + c

Solution:

Here we have:

y - 1 9

y - 1 9 x - 6 = 0

9y - x 54 = 0

-x + 9y - 54 = 0

x - 9y + 54 = 0

x - 9y = 54

Which is the required standard form of the given slope intercept equation.

The slope intercept form to standard form calculator also does the same calculations but saving your precious time and generating instant results.

FAQ’s:

How does slope intercept form work?

As we know that the slope intercept form is given as follows:

y = mx + c

Now if you look at the equation above, the subscript ‘m’ represents the slope of the line and is multiplied by the x (independent variable). The constant b represents the value of the dependent variable which is y. In actual, b is a point where the line touches the vertical y-axis. This is how the slope intercept form works and helps you to draw linear standard equations.

Is slope-intercept form and point-intercept form the same?

No. A slope-intercept form is considered as the particular case of the point slope form. The point under consideration in point slope form is y. So, for converting a standard form to point slope form, you first convert it into the slope-intercept form. After that, moving b to the left side of the equation yields the point-slope form.

What is the basic difference between slope and the intercept?

In graphical analysis, the slope of a particular line displays its steepness. While on the other hand, the intercept indicates the point where the line intersects the x-axis or y-axis. The linear relationship among the slope and the intercept gives us the average changing rate.

What is the point slope standard form?

For linear equations, the point slope in its general form is given as follows:

y - y₁ = m (x - x₁)

The purpose of this form is to find the point on the line.

References:

From the source of Wikipedia: Linear equation, Linear function, Geometric interpretation, Equation of a line

From the source of Lumen Learning: Equations of Lines, The Point-Slope Formula, Standard Form of a Line, Vertical and Horizontal Lines, Parallel and Perpendicular Lines