Question

the graph of a line in the xy-plane has slope 2 and contains the point (1,8). the graph of a second line passes through the points (1,2)&(2,1). it the 2 lines intersect at the point (a,b), what is the value of a+b?

Answer 1

line 1:
slope 2, point(1,8)
hence we have its equation:
y - y1 = m(x - x1)
y - 8 = 2(x - 1)
y = 2x + 6

line 2:
point1(1, 2), point2(2, 1)
hence its slope is:
m = (1 - 2)/(2 - 1) = -1
y - 2 = -1(x - 1)
y = -x + 3

if lines intersect, we can equal both equations and find the point:
y = y
2x + 6 = -x + 3
3x = -3
x = -1
and substitute to find y:
y = -x + 3 = 1 + 3 = 4
therefore the intersection point is (-1, 4), and -1 + 4 = 3