Assess Yourself

Are you ready to take this lesson's quiz? The questions below will help you find out. Make sure you understand why each correct answer is correct—if you don't, review that part of the lesson.

$ m = - \frac{1}{4} $
$ m = - \frac{2}{5} $
$ m = - \frac{3}{2} $
$ m = x $

For an equation written in point-slope form, you can look for the value of $ m $, $ y - y_{1} = \require{color}\colorbox{yellow}{$ m $}\left( x - x_{1} \right),\ $to determine the slope.

When an equation is written in point-slope form, $ y - y_{1} = \require{color}\colorbox{yellow}{$ m $}(x - x_{1}) $, the value of the slope is represented by $ m $.

For an equation written in point-slope form, you can look for the value of $ m $, $ y - y_{1} = \require{color}\colorbox{yellow}{$ m $}\left( x - x_{1} \right),\ $to determine the slope.

$ ( - 2,\ 8) $
$ (2, - 4) $
$ ( - 2, - 8) $
$ (2,\ 8) $

When an equation is written in point-slope form, $ y - \require{color}\colorbox{yellow}{$ y_{1} $} = m\left( x - \require{color}\colorbox{yellow}{$ x_{1} $} \right), $ the ordered pair $ (x_{1},\ y_{1}) $ lies along the line.

$ (2,\ 4) $
$ (0,\ 2) $
$ (4,\ 0) $
$ (4,\ 2) $

Substitute $ y = 0 $ into the equation and then solve for $ x $. This is the value of the $ x $-coordinate at the $ x $-intercept. The value of the $ y $-coordinate is $ 0 $.

Substitute $ y = 0 $ into the equation and then solve for $ x $. This is the value of the $ x $-coordinate at the $ x $-intercept. The value of the $ y $-coordinate is $ 0 $. $ y = - \frac{1}{2}x + 2 $$ 0 = - \frac{1}{2}x + 2 $$ 0 - 2 = - \frac{1}{2}x + 2 - 2 $$ - 2 = - \frac{1}{2}x $$ - 2( - 2) = - \frac{1}{2}x( - 2) $$ 4 = x $

Substitute $ y = 0 $ into the equation and then solve for $ x $. This is the value of the $ x $-coordinate at the $ x $-intercept. The value of the $ y $-coordinate is $ 0 $.

$ (x,\ y) $
$ (x,\ 0) $
$ (0,\ 0) $
$ (0,\ y) $

This ordered pair represents any coordinate pair on the coordinate plane.

This ordered pair represents an $ x $-intercept.

These are the coordinates of the origin.

For a $ y $-intercept, the value of the $ x $-coordinate is always $ 0 $. The value of the $ y $-coordinate can be any real number.

$ y = - \frac{1}{2}x + 9 $
$ y = - \frac{1}{2}x - 15 $
$ y = - \frac{1}{2}x + 12 $
$ y = - \frac{1}{2}x - 6 $

Distribute the value $ - \frac{1}{2} $ through the parentheses on the right-hand side of the equation before collecting like terms.

Start by simplifying the expression $ y - ( - 9) $ to $ y + 9 $.

Remember that the expression $ y - ( - 9) $ simplifies to $ y + 9 $.

Start by simplifying any double negatives. Then, distribute on the right-hand side of the equation. Finish by collecting the like terms. $ y - ( - 9) = - \frac{1}{2}(x - 6) $$ y + 9 = - \frac{1}{2}x + 3 $$ y + 9 - 9 = - \frac{1}{2}x + 3 - 9 $$ y = - \frac{1}{2}x - 6 $

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