Question

A line connecting the points (-3,0) and (x, -6)has slope -1. Determine x.

Answer 1

x = 3

Explanation:

The given slope and point can be used to write the equation of the line using the point-slope form. To find x for a given y, we can solve that equation.

__

setup

The point-slope form of the equation for a line is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

For (h, k) = (-3, 0), and m = -1, the equation is ...

y -0 = -1(x -(-3))

y = -x -3

We want x when y = -6, so this becomes ...

-6 = -x -3

solution

Adding x+6 to both sides of the equation, we get ...

(x +6) -6 = -x -3 +(x +6)

x = 3 . . . . . . . simplify

Answer 2

x=3

Explanation:

We can use the slope formula to help complete this question

m = (y2-y1)/(x2-x1)

-1 = ( -6-0)/(x- -3)

-1 = -6/ (x+3)

Multiply each side by (x+3)

-x-3 = -6

Add 3 to each side

-x -3+3 = -6+3

-x =-3

Multiply each side by -1

x = 3