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 [tex]\frac{2}{3}[/tex]
To find: y
The slope of line is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text {Here }\left(x_{1}, y_{1}\right)=(9, y) \text { and }\left(x_{2}, y_{2}\right)=(-6,3)[/tex]
Substituting the values in formula,
[tex]m=\frac{3-y}{-6-9}[/tex]
Substitute [tex]m = \frac{2}{3}[/tex]
[tex]\frac{2}{3}=\frac{3-y}{-6-9}[/tex]
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
