Question

The lines y=4x-7 and 2x+3y-21=0 intersect at a point A. The point B has coordinates (-2, 8).Find the equation of the lines that passes through the points A and B

Answer 1

for intersection , use substitution

in the 2nd equation
2x + 3y - 21 = 0
2x + 3(4x-7) = 21
2x + 12x - 21 = 21
14x = 42
x = 3
y = 4(3) -7 = 5

so we have the line going through (3,5) and (-2,8)
slope of line = (8-5)/(-2-3) = -3/5

using (3,5)

y-5 = (-3/5)(x-3)
times 5
5y - 25 = -3(x-3)
5y - 25 = -3x + 9

3x + 5y = 34