Question

A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a?

Answer 1

First, we need to find the slope:
m=rise/run OR

`m= (y_2-y_1)/(x_2-x_1)`
m=(2+2)/(-6-2)
m=4/-8
m=-1/2

second we need to find the equation for the line using point-slope form:

`y-y_1=m(x-x_1)`

y-(-2)=-(1/2)(x-2)

`y+2= -(1)/(2)x+1`

`y=- (1)/(2)x-1`

to find "a" we plug in the given y value and solve for x (in this case x=a):


`-4=- (1)/(2)x-1`

`-3=- (1)/(2) x`

`-3(-2)=(- (1)/(2) x)( -2)`

`6=x`

so, a=6 and the point becomes (6,-4)