Question

A line contains (9,y) and (-6,3). It has slope 2/3, find y

Answer 1

The line contains (9,y) and (-6,3) Then y is 13

Solution:

Given that a line contains (9, y) and (-6, 3)

Slope of line is $\frac{2}{3}$

To find: y

The slope of line is given as:

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

$\text {Here }\left(x_{1}, y_{1}\right)=(9, y) \text { and }\left(x_{2}, y_{2}\right)=(-6,3)$

Substituting the values in formula,

$m=\frac{3-y}{-6-9}$

Substitute $m = \frac{2}{3}$

$\frac{2}{3}=\frac{3-y}{-6-9}$

2(-6 - 9) = 3(3 - y)

Multiplying the terms with terms inside bracket

-12 - 18 = 9 - 3y

Move the variable to one side

-30 = 9 - 3y

On solving we get,

3y = 30 + 9

3y = 39

Divide both sides by 3, we get

y = 13

Thus y = 13