Question

On a coordinate plane, a line with negative slope goes through (negative 8, 6) and (4, negative 4). A point is at (negative 6, 10).

Which is the ordered pair for the point on the x-axis that is on the line parallel to the given line and through the given point (–6, 10)?

(6, 0)
(0, 6)
(−5, 0)
(0, −5)

Answer 1

First find the slope of the given line:
m = (−4 − 6)/(4 − (−8)) = −10/12 = −5/6.

The parallel line through (−6, 10) has equation
y − 10 = (−5/6)(x + 6).

Set y = 0 to find the x-intercept:
−10 = (−5/6)(x + 6) → multiply by 6: −60 = −5(x + 6) → x + 6 = 12 → x = 6.

So the ordered pair is (6, 0).