Question

A line goes through the point (–4,–2) and has an x-intercept of –1.

Which point also lies on the line?
(–6,–5)
(3,2)
(4,5)
(5,4)

Answer 1

(5,4)

Explanation:

thanks to the second information we know that a certain second point of the line is (-1,0)

Now we can use a formula to find the equation of the line, that is

(y-y1)/(y2-y1) = (x-x1)/(x2-x1) where x and y 1 and 2 are the coordinates of the points.

(y+2)/2 = (x+4)/(-1+4)

y+2/2 = (x+4)/ 3

3y+6 = 2x+8

2x-3y+2 = 0

now we have to find the point that make true the equation (we have to sobstitute x and y with the coordinates of the given points)

1) -12 +15 + 2 = 0 ; 3 = 0 (wrong)

2) 6-4+2 = 0 ; 4 = 0 (wrong)

3) 8-15+2 = 0 ; -5 = 0 (wrong)

4) 10-12+2 = 0 ; 0=0 (true)

so (5,4) is the correct answer