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
`(2)/(3)`

To find: y

The slope of line is given as:

`m=(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=(3-y)/(-6-9)`

Substitute
`m = (2)/(3)`

`(2)/(3)=(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