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The worksheets on this page include 2 sets of practice problems involving the conversion of linear equations in slope intercept form to standard form and vice versa. Each set includes 8 worksheets each with different levels of difficulty. Working with both forms helps students understand the relationship between slope, y-intercept, and linear equations. If you’re ready, go ahead and print any of the worksheets below. Answer keys are available on the second page of each PDF file. To know more about the slope-intercept and standard form, and how to convert each form to the other, continue reading below…

The slope-intercept form is a way of writing the equation of a straight line (i.e., a linear equation). It’s expressed as:

Here’s what the formula mean:

- y and x are the coordinates of any point on the line.
- m is the slope of the line. It represents the rate of change, or how much y changes for a given change in x. It’s calculated as the rise over the run (the vertical change divided by the horizontal change).
- b is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of y when x is 0. It provides a starting point for graphing the line and is often a key piece of information for understanding the position of the line.

So, with this form, you can easily see the slope and the y-intercept of the line.

Examples of linear equations in slope intercept form:

y = 3x - 3

y = -4x + 5

y = 10x - 8

y = 12x + 6

The standard form of a linear equation is another way to express the equation of a straight line. It’s written as:

Here’s what the components mean:

- A, B, and C are constants (integers only).
- x and y are the variables representing the coordinates of any point on the line.

In standard form:

- A, B, and C are typically integers, and A is usually non-negative.
- The coefficients A and B should be integers, and A is often made positive for convention.
- C is the constant term that can be any integer

Examples of linear equations in standard form:

3x + 4y = 8

2x - 3y = -6

5x + 8y = 12

7x - 2y = 1

Converting a linear equation from slope-intercept form y = mx + b to standard form Ax + By = C involves a few steps. Let’s break it down.

- Start with the slope-intercept form equation: y = mx + b
- Move the mx and y terms to the same side of the equal side. To do this, rearrange the equation by subtracting the mx term from both sides. When we do that, our mx‘s cancel out and we’re left with:: −mx + y = b
- Multiply through by -1 if necessary to make mx positive: mx − y = −b
- In here mx=A ; y=B ; and b=C. Write in standard form: Ax - By = -C

Remember:

Ensure that A is non-negative. If not, multiply through by -1 to correct it.

A, B, and C should be integers, so eliminate any fractions or decimals if needed.

Simplify the coefficients if possible.

Let’s try some examples…

**Example 1:** Convert the linear equation y = 2x − 3 from slope-intercept form to standard form.

- Start with the given equation: y = 2x − 3
- Move 2x to the left side: −2x + y = −3
- To make -2x positive, multiply through by -1: 2x − y = 3
- So, the standard form of y = 2x − 3 is: 2x − y = 3

**Example 2:** Convert the linear equation y = -5x + 7 from slope-intercept form to standard form.

- Start with the given equation: y = -5x + 7
- Move -5x to the left side: 5x + y = 7
- So, the standard form of y = -5x + 7 is: 5x + y = 7

**Example 3:** Convert the linear equation y = (-3/2)x + 2 from slope-intercept form to standard form.

- Start with the given equation: y = (-3/2)x + 2
- Move (-3/2)x to the left side: (3/2)x + y = 2
- Multiply both sides by 2: 3x + 2y = 4
- So, the standard form of y = (-3/2)x + 2 is: 3x + 2y = 4

Similarly, converting a linear equation from standard form Ax + By = C to slope-intercept form y = mx + b also involves a few steps. These are the following:

- Start with the Standard Form: Ax + By = C
- Isolate the y term by subtracting Ax from both sides, we get: By = −Ax + C
- Solve for y by dividing every term by B, we get: y = -Ax/B + C/B
- In here A=mx ; B=y ; and C=b. Write in slope intercept form: y = -mx + b
- Simplify if needed.

You can use the skills of solving for a variable to change any linear equation from standard form into slope-intercept form. All that is required is that you solve for y then arrange them so that the term with x in it comes first.

**Example 1:** Convert the linear equation 5x + y = 7 from standard form to slope-intercept form.

- Start with the given equation: 5x + y = 7
- Move 5x to the right side by subtracting 5x from both sides we get: y = −5x + 7
- So, the slope-intercept form of 5x + y = 7 is y = -5x + 7

**Example 2:** Convert the linear equation 6x - y = 3 from standard form to slope-intercept form.

- Start with the given equation: 6x - y = 3
- Move 6x to the right side by subtracting 6x from both sides, we get: -y = −6x + 3
- To make y positive, multiply through by -1: y = 6x - 3
- So, the slope-intercept form of 6x - y = 3 is y = 6x - 3

**Example 3:** So, the slope-intercept form of 6x - y = 3 is y = 6x - 3.

- Start with the given equation: 12x + 4y = 8
- Move 12x to the right side by subtracting 12x from both sides, we get: 4y = −12x + 8
- Solve for y by dividing every term by 4: 4y/4 = −12x/4 + 8/4
- Simplify the y-intercept term: y = −3x + 2
- So, the slope-intercept form of 12x + 4y = 8 is y = −3x + 2.

If you are looking for more exercises, be sure to check out our main linear equation worksheets page! You'll find lots of other practice problems involving linear equations like Graphing Linear Equations, Finding the Equation of a Line, Graphing Linear Inequalities, and much more… You will also find a Slope Intercept Form Anchor Chart that you can use for teaching how to graph linear equations.