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. But a direct use of this equation to slope intercept form calculator will confuse you regarding the terms involved in calculations.

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:

$$ y = mx + c $$ 

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:

$$ 2x - 9y = 15 $$

$$ -9y = -2x + 15 $$

$$ -9y = -\left(2x + 15\right) $$

$$ 9y = 2x - 15 $$

$$ y = \frac{2x - 15}{9} $$

$$ y = \frac{2x}{9} - \frac{15}{9} $$

$$ y = 0.222x -1.666 $$

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:

$$ 0 = mx +c $$

$$ x = -\frac{c}{m} $$

$$ x = -\frac{1.666}{0.222} $$

$$ x = 7.5 $$

$$ Y-intercept = -1.666 $$

$$ \text{Percentage Grade} = Slope * 100 $$

$$ \text{Percentage Grade} = 0.222 * 100 $$

$$ \text{Percentage Grade} = 22.22% $$

For angle, we have:

$$ \theta = arctan\left(\frac{y}{x}\right) $$

$$ \theta = arctan\left(\frac{-1.666}{7.5}\right) $$

$$ \theta = arctan\left(0.222\right) $$

$$ \theta = 12.51^\text{o} $$

Example # 02:

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

$$ y = \frac{1}{9}x + c $$

Solution:

Here we have:

$$ y - \frac{1}{9}x - 6 = 0 $$

$$ 9y - x 54 = 0 $$

$$ -x + 9y - 54 = 0 $$

$$ x - 9y + 54 = 0 $$

$$ x - 9y = 54 $$

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:

$$ y - y_{1} = m\left(x - x_{1}\right) $$

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