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Algebra 1

1.12.4 Writing Equations in Different Forms

Algebra 11.12.4 Writing Equations in Different Forms

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Activity

Three Different Forms of Linear Equations

Work with a partner to answer 1 - 3.

1.

What is the slope-intercept form of a linear equation?

2.

What is the point-slope form of a linear equation?

3.

What is the standard form of a linear equation?

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 y4=3(x+1)y4=3(x+1).

4.

Write the equation in slope-intercept form.

5.

Write the equation in standard form.

6.

Write 4x6y=124x6y=12 in slope-intercept form.

Self Check

Which of the following is equivalent to y=4x+5y=4x+5 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 yy-intercept of 7.

Slope-Intercept Form

Slope-intercept form is y=mx+by=mx+b where m is the slope and bb is the yy-intercept.

Substitute m=2m=2 and b=7b=7 to have the equation y=2x+7y=2x+7.

Standard Form

Write the same equation in standard form.

Standard form is Ax+By=CAx+By=C.

Remember that AA can not be negative and there should not be any fractions or decimals.

For this form, rearrange slope-intercept form to lead with the xx term:

Step 1 - Bring the xx and yy terms on the left side.

y2x=2x2x+7y2x=2x2x+7

Step 2 - Simplify.

2x+y=72x+y=7

Step 3 - Divide all terms by -1 so that AA is not negative.

2x1+y1=712x1+y1=71

Step 4 - Simplify.

2xy=72xy=7

Point-Slope Form

Point-Slope form is yy1=m(xx1)yy1=m(xx1).

Substitute the slope in for mm and the point in for (x1,y1)(x1,y1).

m=2m=2, x1=0x1=0, y1=7y1=7

y7=2(x0)y7=2(x0)

Notice this can easily be written in slope-intercept form by solving for yy:

y7=2(x0)y7=2x0y7+7=2x0+7y=2x+7y7=2(x0)y7=2x0y7+7=2x0+7y=2x+7

Standard Form to Slope-Intercept Form

Standard form can also be rearranged into slope-intercept form.

Write 3x5y=143x5y=14 in slope-intercept form.

Work to solve for yy.

Step 1 - Bring the xx term to the right side with the constant.

3x3x5y=143x3x3x5y=143x

Step 2 - Simplify.

5y=143x5y=143x

Step 3 - Divide by the coefficient of yy.

5y5=14535x5y5=14535x

Step 4 - Simplify and write in the correct order.

y=35x+145y=35x+145

Try it

Try It: Writing Equivalent Linear Forms

Write the equation 3x+8y=243x+8y=24 in slope-intercept form.

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