How do you find the slope and intercept of $-3x + 2y = 8$ ?

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Answer 1 · 2017-01-07T16:51:56

To find the slope and y-intercept of this line convert it to the slope-intercept form. See full explanation below.

To find the slope and y-intercept of this line convert it to the slope-intercept form.

The slope-intercept form of a linear equation is:

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

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

We can solve this equation for $y$ to get it into this format.

$-3x + 2y = 8$

$-3x + color(red)(3x) + 2y = color(red)(3x) + 8$

$0 + 2y = 3x + 8$

$2y = 3x + 8$

$(2y)/color(red)(2) = (3x + 8)/color(red)(2)$

$(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = (3x)/color(red)(2) + 8 /color(red)(2)$

$y = 3/2x + 4$

or

$y = color(red)(3/2)x + color(blue)(4)$

So the slope is $m = color(red)(3/2)$

And the y-intercept is $b = color(blue)(4)$

How do you find the slope and intercept of -3x + 2y = 8-3x + 2y = 8?