# How to Convert a Linear Equation in Standard Form to Slope-Intercept Form?

The standard form and slope-intercept form are ways of writing linear equations. In this guide, you learn more about converting standard form to slope-intercept form. The equation with the highest degree $$1$$ is known as the linear equation. There are different formulas available to find the equation of a straight line.

## A step-by-step guide toconverting standard form to slope-intercept form

The equation of a line is the equation that is satisfied by each point that lies on that line. There are several ways to find this equation in a straight line, as follows:

• Slope-intercept form
• Point slope form
• Two-point form
• Intercept form

### Standard form

The standard form of linear equations is also known as the general form and is represented as:

$$Ax+By=C$$

where $$A, B$$, and $$C$$ are integers, and the letters $$x$$ and $$y$$ are the variables.

### Slope-intercept form

The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we need to know the slope of the line and the intercept cut by the line with the $$y$$-axis. Let’s consider a straight line of slope $$m$$ and $$y$$-intercept $$b$$. The slope-intercept form equation for a straight line with a slope, $$m$$, and $$b$$ as the $$y$$-intercept can be given as $$y=mx + b$$.

How to convert standard form to slope-intercept form?

By rearranging and comparing, we can convert the equation of a line given in the standard form to slope-intercept form. We know that the standard form of the equation of a straight line represents as follows:

$$Ax + By + C = 0$$

Rearranging the terms to find the value of $$y$$, we get,

$$B×y=-Ax – C$$
$$y = (-\frac{A}{B})x + (-\frac{C}{B})$$

where, $$(-\frac{A}{B})$$ makes the slope of the line and $$(-\frac{C}{B})$$ is the $$y$$-intercept.

### Converting Standard Form to Slope-Intercept Form – Example 1:

Write the following standard form equation of a line in slope-intercept form. $$x-2y=-6$$

Solution:

Subtract $$x$$ from each side.

$$-2y = -x-6$$

Multiply each side by $$-1$$.

$$2y = x + 6$$

Divide each side by $$2$$.

$$y = \frac{(x + 6)}{2}$$

$$y=\frac{x}{2}+\frac{6}{2}$$

$$y=\frac{x}{2}+ 3$$

## Exercises forConverting Standard Form to Slope-Intercept Form

### Write the standard form equation of a line in slope-intercept form.

1. $$\color{blue}{7x-2y=5}$$
2. $$\color{blue}{2x-6y=-11}$$
3. $$\color{blue}{3x-3y=12}$$
4. $$\color{blue}{12x-12y=5}$$
1. $$\color{blue}{y=\frac{7}{2}x-\frac{5}{2}}$$
2. $$\color{blue}{y=\frac{1}{3}x+\frac{11}{6}}$$
3. $$\color{blue}{y=x-4}$$
4. $$\color{blue}{y=x-\frac{5}{12}}$$

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