Question

Write the equation of the line, given the y- and x- intercepts.

y-intercept (0,-6)
x-intercept (-2,0)

Answer 1

y = -3x - 6

Explanation:

Treat (0,-6) and (-2,0) as points on the line; it is not essential to recognize that they represent the x- and y-intercepts. As we go from (-2,0) to (0,-6), x increases by 2 and y decreases by 6. Thus, the slope of this line is m = rise / run = -6/2 = -3.

Write out the slope-intercept form: y = mx + b. Now subst. -3 for m, -6 for y and 0 for x, obtaining: -6 = -3(0) + b. Then b = -6, and the equation of this line is therefore y = -3x - 6.

Check: If x=0, is y=-6? Yes. If y = 0, is x= -2? Yes.