Question

the straight L has gradient 3 and passes through the point A(-6,4).
a) find an equation for L in the form y=mx+c
b) straight line R has the equation in the form of -7y+x+14=0. Given that R crosses the y-axis at the point B and intersects L at the point C, find the coordinates of B and C

Answer 1

equation for L:
y = 3x + b, but (-6,4) lies on it, so
4 = 3(-6) + b
b = 22
equation: y = 3x + 22

y-intercept of x-7y+14=0
let x = 0
-7y = -14
y = 2
so B is (0,2)

intersection of L and R:
sub L into R
x - 7y = -14
x - (3x+22) = -14
-2x = 8
x = -4 , then y = -12+22=10

so point C is (10,-4)

check my arithmetic.