How do you find the slope and y-intercept for the graph of the equation: 9x - 3y = 81?

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Answer 1 · 2016-12-27T00:07:43

graph{y = 3x - 27 [-5, 10, -30, 5]}

The slope is $3$ $color(red)(3)$ and the y-intercept is $- 27$ $color(blue)(-27)$ or ( $0, - 27$ $color(blue)(0, -27)$ )

To find the slope and y-intercept of this equation we must transform it into the slope-intercept form.

The slope-intercept form of a linear equation is:

$y = m x + b$ $y = color(red)(m)x + color(blue)(b)$

Where $m$ $color(red)(m)$ is the slope and $b$ $color(blue)(b$ is the y-intercept value.

We can solve this equation for $y$ $y$ to transform the equation we have been given in this problem into this form:

$9 x - 3 y = 81$ $9x - 3y = 81$

$9 x - 9 x - 3 y = - 9 x + 81$ $9x - color(red)(9x) - 3y = color(red)(-9x) + 81$

$0 - 3 y = - 9 x + 81$ $0 - 3y = color(red)(-9x) + 81$

$- 3 y = - - 9 x + 81$ $-3y = - color(red)(-9x) + 81$

$\frac{- 3 y}{- 3} = \frac{- 9 x + 81}{- 3}$ $(-3y)/color(green)(-3) = (color(red)(-9x) + 81)/color(green)(-3)$

$(color(green)(cancel(color(black)(-3)))y)/cancel(color(green)(-3)) = (color(red)(-9x) + 81)/color(green)(-3)$

$y = (color(red)(-9x) + 81)/color(green)(-3)$

$y = color(red)(-9x)/color(green)(-3) + 81/color(green)(-3)$

$y = 3x - 27$

Therefore the slope is $color(red)(3)$ and the y-intercept is $color(blue)(-27)$ or ( $color(blue)(0, -27)$ )