Question

Write the equation of the line that passes through (-9,-4) and (-6,-2) in slope-intercept form.(Fraction not division)

a. y= (3/2x) +7b. y=−(2/3x)−6c. y=(2/3x)−6d. y=(2/3x)+2

Answer 1

In general the line through (a,b) and (c,d) is

`(c-a)(y-b)=(d-b)(x-a)`

Can you see why?

Here we have

`(-6 - -9)(y - -4) = (-2 - - 4)(x- -9)`

`3(y+4)= 2(x+9)`

`3y + 12 = 2x + 18`

`3y = 2x + 6`

`y = \frac 2 3 x + 2`

That's choice d, though I would parenthesize it as y=(2/3)x+2 so it doesn't look like we're dividing by x.