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)#