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) =
`(5)/(4)`

To find the missing coordinate r:

Slope formula:

`$m=(y_(2)-y_(1))/(x_(2)-x_(1))$`

Substitute the given values in the formula.

`$(5)/(4)=(r-1)/(-7-(-15))`

`$(5)/(4)=(r-1)/(-7+15)`

`$(5)/(4)=(r-1)/(8)`

Do cross multiplication.

`8 * 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.