Converting from Point-Slope to Slope-Intercept Form Practice

Let's Practice

You have learned that each line in the coordinate plane has both an $ x $- and a $ y $-intercept and that a single line can be represented by many different point-slope equations. The point-slope form of a line is $ y - y_{1} = m(x - x_{1}) $. You can follow a series of steps to rewrite each point-slope equation in slope-intercept form, $ y = mx + b $. It's your turn to practice this skill!

How well can you convert the equation of a line from point-slope form to slope-intercept form? Use the activity below to practice. Convert each equation from point-slope form to slope-intercept form. Then, name the $ x $- and $ y $-intercepts of each equation, and check your answer.

Rewrite the equation $ y - ( - 7) = - 2(x - 2) $ in slope-intercept form. Give the coordinates of both its $ x $- and $ y $-intercepts.

$ y = - 2x - 3 $

$ x $-intercept: $ \left( - \frac{3}{2},0 \right) $

$ y $-intercept: $ \left( 0, - 3 \right) $

If you need help arriving at this answer, click the Solution button.

Step 1: Simplify any double negatives.	There is a double negative on the left-hand side of the equation. $ y \ \require{color}\colorbox{yellow}{$ - \left( - 7 \right) $} = - 2\left( x - 2 \right) $ $ y \ \require{color}\colorbox{yellow}{$ + 7 $} = - 2(x - 2) $
Step 2: Distribute on the right-hand side of the equation.	$ y + 7 = - 2\left( x - 2 \right) $ $ y + 7 = - 2x + 4 $
Step 3: Collect the like terms.	$ y + 7 {\color{#A80000}{\ - 7}} = - 2x + 4 {\color{#A80000}{\ - 7}} $ $ y = - 2x - 3 $
Step 4: Read the location of the $ y $-intercept from the equation.	$ \left( 0, - 3 \right) $
Step 5: Solve for the location of the $ x $-intercept.	Substitute $ y = 0 $ into the slope-intercept form of the equation. $ (0) = - 2x - 3 $ $ 0 {\color{#A80000}{\ +\ 3}} = - 2x - 3 {\color{#A80000}{\ +\ 3}} $ $ 3 = - 2x $ $ - \frac{3}{2} = x $ The $ x $-intercept is $ \left( - \frac{3}{2},0 \right) $.

Rania and Portia are working on the design plans for the drainage systems of the pools in the city of Geocove's waterpark. The maximum rate at which Pool 1 can be drained is represented by the equation $ y - 1800 = - 300(x - 0) $.

Rewrite this equation in slope-intercept form and give the coordinates of both its $ x $- and $ y $-intercepts.

$ y = - 300x + 1800 $

$ x $-intercept: $ \left( 6,0 \right) $

$ y $-intercept: $ \left( 0,\ 1800 \right) $

If you need help arriving at this answer, click the Solution button.

Step 1: Simplify any double negatives.	This equation does not contain any double negatives.
Step 2: Distribute on the right-hand side of the equation.	$ y - 1800 = - 300(x - 0) $ $ y - 1800 = - 300x $
Step 3: Collect the like terms.	$ y - 1800 {\color{#A80000}{\ +\ 1800}} = - 300x {\color{#A80000}{\ +\ 1800}} $ $ y = - 300x + 1800 $
Step 4: Read the location of the $ y $-intercept from the equation.	$ \left( 0,\ 1800 \right) $
Step 5: Solve for the location of the $ x $-intercept.	Substitute $ y = 0 $ into the slope-intercept form of the equation. $ \left( 0 \right) = - 300x + 1800 $ $ 0 {\color{#A80000}{\ - 1800}} = - 300x + 1800 {\color{#A80000}{\ - 1800}} $ $ - \frac{1800}{ {\color{#A80000}{- 300}}} = - \frac{300x}{ {\color{#A80000}{- 300}}} $ $ 6 = x $ The $ x $-intercept is $ \left( 6,0 \right) $.

Rewrite the equation $ y - 10 = \frac{1}{4}(x - 16) $ in slope-intercept form. Give the coordinates of both its $ x $- and $ y $-intercepts.

$ y = \frac{1}{4}x + 6 $

$ x $-intercept: $ \left( - 24,0 \right) $

$ y $-intercept: $ \left( 0,\ 6 \right) $

If you need help arriving at this answer, click the Solution button.

Step 1: Simplify any double negatives.	This equation does not contain any double negatives.
Step 2: Distribute on the right-hand side of the equation.	$ y - 10 = \frac{1}{4}\left( x - 16 \right) $ $ y - 10 = \frac{1}{4}x - 4 $
Step 3: Collect the like terms.	$ y - 10 {\color{#A80000}{\ +\ 10}} = \frac{1}{4}x - 4 {\color{#A80000}{\ +\ 10}} $ $ y = \frac{1}{4}x + 6 $
Step 4: Read the location of the $ y $-intercept from the equation.	$ \left( 0,\ 6 \right) $
Step 5: Solve for the location of the $ x $-intercept.	Substitute $ y = 0 $ into the slope-intercept form of the equation. $ (0) = \frac{1}{4}x + 6 $ $ - 6 = \frac{1}{4}x $ $ - 24 = x $ The $ x $-intercept is $ \left( - 24,0 \right) $.

Rania and Portia are working on the design plans for the drainage systems of the pools in Geocove's waterpark. The maximum rate at which Pool 2 can be drained is represented by the equation $ y - ( - 3600) = - 600(x - 13) $.

Rewrite this equation in slope-intercept form and give the coordinates of both its $ x $- and $ y $-intercepts.

$ y = - 600x + 4200 $

$ x $-intercept: $ \left( 7,0 \right) $

$ y $-intercept: $ \left( 0,\ 4200 \right) $

If you need help arriving at this answer, click the Solution button.

Step 1: Simplify any double negatives.	$ y - ( - 3600) = - 600(x - 13) $ $ y + 3600 = - 600(x - 13) $
Step 2: Distribute on the right-hand side of the equation.	$ y + 3600 = - 600\left( x - 13 \right) $ $ y + 3600 = - 600x + 7800 $
Step 3: Collect the like terms.	$ y + 3600 {\color{#A80000}{\ - 3600}} = - 600x + 7800 {\color{#A80000}{\ - 3600}} $ $ y = - 600x + 4200 $
Step 4: Read the location of the $ y $-intercept from the equation.	$ \left( 0,\ 4200 \right) $
Step 5: Solve for the location of the $ x $-intercept.	Substitute $ y = 0 $ into the slope-intercept form of the equation. $ \left( 0 \right) = - 600x + 4200 $ $ - 4200 = - 600x $ $ 7 = x $ The $ x $-intercept is $ \left( 7,0 \right) $.

Rania and Portia are working on the design plans for the drainage systems of the pools in Geocove's waterpark. The maximum rate at which Pool 3 can be drained is represented by the equation $ y - 7200 = - 900(x - 3) $.

Rewrite this equation in slope-intercept form and give the coordinates of both its $ x $- and $ y $-intercepts.

$ y = - 900x + 9900 $

$ x $-intercept: $ \left( 11,0 \right) $

$ y $-intercept: $ \left( 0,\ 9900 \right) $

If you need help arriving at this answer, click the Solution button.

Step 1: Simplify any double negatives.	This equation does not contain any double negatives.
Step 2: Distribute on the right-hand side of the equation.	$ y - 7200 = - 900\left( x - 3 \right) $ $ y - 7200 = - 900x + 2700 $
Step 3: Collect the like terms.	$ y - 7200 = - 900x + 2700 $ $ y = - 900x + 9900 $
Step 4: Read the location of the $ y $-intercept from the equation.	$ \left( 0,\ 9900 \right) $
Step 5: Solve for the location of the $ x $-intercept.	Substitute $ y = 0 $ into the slope-intercept form of the equation. $ (0) = - 900x + 9900 $ $ - 9900 = - 900x $ $ 11 = x $ The $ x $-intercept is $ \left( 11,0 \right) $.

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Step 1: Simplify any double negatives.	There is a double negative on the left-hand side of the equation. \( y \ \require{color}\colorbox{yellow}{$ - \left( - 7 \right) $} = - 2\left( x - 2 \right) \) \( y \ \require{color}\colorbox{yellow}{$ + 7 $} = - 2(x - 2) \)
Step 2: Distribute on the right-hand side of the equation.	\( y + 7 = - 2\left( x - 2 \right) \) \( y + 7 = - 2x + 4 \)
Step 3: Collect the like terms.	\( y + 7 {\color{#A80000}{\ - 7}} = - 2x + 4 {\color{#A80000}{\ - 7}} \) \( y = - 2x - 3 \)
Step 4: Read the location of the \( y \)-intercept from the equation.	\( \left( 0, - 3 \right) \)
Step 5: Solve for the location of the \( x \)-intercept.	Substitute \( y = 0 \) into the slope-intercept form of the equation. \( (0) = - 2x - 3 \) \( 0 {\color{#A80000}{\ +\ 3}} = - 2x - 3 {\color{#A80000}{\ +\ 3}} \) \( 3 = - 2x \) \( - \frac{3}{2} = x \) The \( x \)-intercept is \( \left( - \frac{3}{2},0 \right) \).

Step 1: Simplify any double negatives.	This equation does not contain any double negatives.
Step 2: Distribute on the right-hand side of the equation.	\( y - 1800 = - 300(x - 0) \) \( y - 1800 = - 300x \)
Step 3: Collect the like terms.	\( y - 1800 {\color{#A80000}{\ +\ 1800}} = - 300x {\color{#A80000}{\ +\ 1800}} \) \( y = - 300x + 1800 \)
Step 4: Read the location of the \( y \)-intercept from the equation.	\( \left( 0,\ 1800 \right) \)
Step 5: Solve for the location of the \( x \)-intercept.	Substitute \( y = 0 \) into the slope-intercept form of the equation. \( \left( 0 \right) = - 300x + 1800 \) \( 0 {\color{#A80000}{\ - 1800}} = - 300x + 1800 {\color{#A80000}{\ - 1800}} \) \( - \frac{1800}{ {\color{#A80000}{- 300}}} = - \frac{300x}{ {\color{#A80000}{- 300}}} \) \( 6 = x \) The \( x \)-intercept is \( \left( 6,0 \right) \).

Step 1: Simplify any double negatives.	This equation does not contain any double negatives.
Step 2: Distribute on the right-hand side of the equation.	\( y - 10 = \frac{1}{4}\left( x - 16 \right) \) \( y - 10 = \frac{1}{4}x - 4 \)
Step 3: Collect the like terms.	\( y - 10 {\color{#A80000}{\ +\ 10}} = \frac{1}{4}x - 4 {\color{#A80000}{\ +\ 10}} \) \( y = \frac{1}{4}x + 6 \)
Step 4: Read the location of the \( y \)-intercept from the equation.	\( \left( 0,\ 6 \right) \)
Step 5: Solve for the location of the \( x \)-intercept.	Substitute \( y = 0 \) into the slope-intercept form of the equation. \( (0) = \frac{1}{4}x + 6 \) \( - 6 = \frac{1}{4}x \) \( - 24 = x \) The \( x \)-intercept is \( \left( - 24,0 \right) \).

Step 1: Simplify any double negatives.	\( y - ( - 3600) = - 600(x - 13) \) \( y + 3600 = - 600(x - 13) \)
Step 2: Distribute on the right-hand side of the equation.	\( y + 3600 = - 600\left( x - 13 \right) \) \( y + 3600 = - 600x + 7800 \)
Step 3: Collect the like terms.	\( y + 3600 {\color{#A80000}{\ - 3600}} = - 600x + 7800 {\color{#A80000}{\ - 3600}} \) \( y = - 600x + 4200 \)
Step 4: Read the location of the \( y \)-intercept from the equation.	\( \left( 0,\ 4200 \right) \)
Step 5: Solve for the location of the \( x \)-intercept.	Substitute \( y = 0 \) into the slope-intercept form of the equation. \( \left( 0 \right) = - 600x + 4200 \) \( - 4200 = - 600x \) \( 7 = x \) The \( x \)-intercept is \( \left( 7,0 \right) \).

Step 1: Simplify any double negatives.	This equation does not contain any double negatives.
Step 2: Distribute on the right-hand side of the equation.	\( y - 7200 = - 900\left( x - 3 \right) \) \( y - 7200 = - 900x + 2700 \)
Step 3: Collect the like terms.	\( y - 7200 = - 900x + 2700 \) \( y = - 900x + 9900 \)
Step 4: Read the location of the \( y \)-intercept from the equation.	\( \left( 0,\ 9900 \right) \)
Step 5: Solve for the location of the \( x \)-intercept.	Substitute \( y = 0 \) into the slope-intercept form of the equation. \( (0) = - 900x + 9900 \) \( - 9900 = - 900x \) \( 11 = x \) The \( x \)-intercept is \( \left( 11,0 \right) \).

How well can you rewrite a point-slope equation into slope-intercept form?

Let's Practice

Rewrite the equation \( y - ( - 7) = - 2(x - 2) \) in slope-intercept form. Give the coordinates of both its \( x \)- and \( y \)-intercepts.

Rewrite this equation in slope-intercept form and give the coordinates of both its \( x \)- and \( y \)-intercepts.

Rewrite the equation \( y - 10 = \frac{1}{4}(x - 16) \) in slope-intercept form. Give the coordinates of both its \( x \)- and \( y \)-intercepts.

Rewrite this equation in slope-intercept form and give the coordinates of both its \( x \)- and \( y \)-intercepts.

Rewrite this equation in slope-intercept form and give the coordinates of both its \( x \)- and \( y \)-intercepts.