Question

Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3

Answer 1

General formula of a line:
y = mx+c
Where m is the gradient and c is the y-intercept.

A line with a slope of 2 has the formula:
y = 2x + c -------------------------(1)

We can re-arrange the equation 2x-3y=6 to get:
3y = 2x - 6
Sub x = 3 into this equation to get:
y = 0

Hence the unknown line passes through the point (3,0). Sub this point into equation (1) to get:

0 = 6 + c

c = -6

Hence the equation of the line is y = 2x - 6.