Question

One line passes through the points (−1,6) and (2,0). A second line passes through the points (−5,5) and (−1,9). At what point do the two lines intersect

Answer 1

(-2,8)

Explanation:

Slope m = (y2-y1)/(x2-x1)

Line 1: m = (0 - 6)/(2 - -1) = -6/3 = -2

y = mx+ b => y = -2x + b => 0 = -2(2) + b => 0 = -4 + b => b = 4

y = -2x + 4

Line 2: m = (9 - 5)/(-1 - -5) = 4/4 = 1

y = mx + b => y = x + b => 9 = -1 + b => b = 10

y = x + 10

When the 2 line intersects, they will same the same (x,y)

so line 1 = line 2

-2x + 4 = x + 10

-2x - x = 10 - 4

-3x = 6

x = -2

y = -2x + 4 = -2(-2) + 4 = 8

so the lines intersect at (-2,8)