Question

The points (-6, r) and (6,3) lie on a line with slope 3/4. Find the missing coordinate r.

Answer 1

Answer:

r = -6

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope and b is the y-intercept.

Slope 3/4

This means that $m = \frac{3}{4}$, and thus:

$y = \frac{3}{4}x + b$

(6,3)

This means that when $x = 6, y = 3$. We use this to find b. So

$y = \frac{3}{4}x + b$

$3 = \frac{3}{4}(6) + b$

$b = 3 - \frac{18}{4} = \frac{12}{4} - \frac{18}{4} = -\frac{6}{4}$

So

$y = \frac{3}{4}x - \frac{6}{4} = \frac{3x - 6}{4}$

(-6, r)

r is y when $x = -6$. So

$y = \frac{3(-6) - 6}{4} = -6$

So r = -6.