Question

The points , (−15,1) and , (−7,r) lie on a line with slope 5/4. Find the missing coordinate r. Click image to enlarge

Answer 1

The missing coordinate r is 11.

Solution:

Given points are (–15, 1) and (–7, r).

$x_{1}=-15, x_{2}=-7, y_{1}=1 \text { and } y_{2}=7$

Slope (m) = $\frac{5}{4}$

To find the missing coordinate r:

Slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute the given values in the formula.

$\frac{5}{4}=\frac{r-1}{-7-(-15)}$

$\frac{5}{4}=\frac{r-1}{-7+15}$

$\frac{5}{4}=\frac{r-1}{8}$

Do cross multiplication.

$8 \times 5=4(r-1)$

40 = 4r – 4

Add 4 on both side of the equation.

44 = 4r

Divide by 4 on both side of the equation.

11 = r

⇒ r = 11

Hence the missing coordinate r is 11.