Activity
Three Different Forms of Linear Equations
Work with a partner to answer 1 - 3.
What is the slope-intercept form of a linear equation?
Compare your answer:
What is the point-slope form of a linear equation?
Compare your answer:
What is the standard form of a linear equation?
Compare your answer:
Using the Different Forms to Write Equivalent Equations
Linear equations can be written in the different forms to create linear equations. Use the linear equation forms from 1 - 3 to help you complete the rest of the activity. Remember to show all of your work on your paper and to use inverse operations to move terms to different sides of the equation.
For 4 - 5, use the equation .
Write the equation in slope-intercept form.
Compare your answer:
Write the equation in standard form.
Compare your answer:
Write in slope-intercept form.
Compare your answer:
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Self Check
Which of the following is equivalent to in standard form?
Additional Resources
Writing Equivalent Linear Forms
Write an equation of a line in all three forms that has a slope of 2 and a -intercept of 7.
Slope-Intercept Form
Slope-intercept form is where m is the slope and is the -intercept.
Substitute and to have the equation .
Standard Form
Write the same equation in standard form.
Standard form is .
Remember that can not be negative and there should not be any fractions or decimals.
For this form, rearrange slope-intercept form to lead with the term:
Step 1 - Bring the and terms on the left side.
Step 2 - Simplify.
Step 3 - Divide all terms by -1 so that is not negative.
Step 4 - Simplify.
Point-Slope Form
Point-Slope form is .
Substitute the slope in for and the point in for .
, ,
Notice this can easily be written in slope-intercept form by solving for :
Standard Form to Slope-Intercept Form
Standard form can also be rearranged into slope-intercept form.
Write in slope-intercept form.
Work to solve for .
Step 1 - Bring the term to the right side with the constant.
Step 2 - Simplify.
Step 3 - Divide by the coefficient of .
Step 4 - Simplify and write in the correct order.
Try it
Try It: Writing Equivalent Linear Forms
Write the equation in slope-intercept form.
Compare your answer: