Standard & Slope-Intercept Forms Worksheets

Examples, solutions, videos, and worksheets to help grade 7 students learn how to convert between standard form and slope-intercept form.

How to convert between standard form and slope-intercept form?

There are three sets of Standard & Slope-Intercept Forms worksheets:

• Convert from standard form to slope-intercept form
• Convert from slope-intercept form to standard form
• Convert between standard form and slope-intercept form

The slope-intercept form and the standard form are two common ways to express the equations of straight lines in two-dimensional Cartesian coordinates.

1. Standard Form (Ax + By = C): In the standard form, the equation of a line is expressed as:
   Ax + By = C

• A, B, and C are constants, typically integers.
• A and B cannot both be zero (otherwise, it would not represent a line).

1. Slope-Intercept Form (y = mx + b): In this form, the equation of a line is expressed as:
   y = mx + b

• y and x are variables representing the coordinates of points on the line.
• m is the slope of the line, indicating how steep the line is.
• b is the y-intercept, representing the point where the line crosses the y-axis.

The slope-intercept form is useful for quickly determining the slope and y-intercept of a line, making it easy to graph and interpret.

Converting Between Forms:
You can convert between the slope-intercept form and the standard form.
To convert from standard form to slope-intercept form, you can solve for y in terms of x.
To convert from slope-intercept to standard form, you can multiply both sides of the equation by a common multiple of the denominators to clear the fractions.

Here are examples:

Standard Form to Slope-Intercept Form:
2x - 3y = 6
Solve for y in terms of x:
-3y = -2x + 6
Divide by -3:
y = (2/3)x - 2

Slope-Intercept to Standard Form:
y = (3/4)x - 2
Multiply both sides by 4 to clear the fraction:
4y = 3x - 8
Rearrange to standard form:
3x - 4y = 8

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Standard & Slope-Intercept Forms Worksheets.

More Standard & Slope-Intercept Forms Worksheets

Printable
(Answers on the second page.)
Standard & Slope-Intercept Forms Worksheet #1 (standard form to slope-intercept)
Standard & Slope-Intercept Forms Worksheet #2 (slope-intercept to standard form)
Standard & Slope-Intercept Forms Worksheet #3 (convert between both forms)

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