Given:
A line passes through the points (9,9) and [tex](x_2,-1)[/tex].
The slope of the line is [tex]\dfrac{5}{6}[/tex].
To find:
The value of [tex]x_2][/tex].
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The line passes through the points (9,9) and [tex](x_2,-1)[/tex]. So, the slope of the line is:
[tex]m=\dfrac{-1-9}{x_2-9}[/tex]
[tex]m=\dfrac{-10}{x_2-9}[/tex]
It is given that the slope of the line is [tex]\dfrac{5}{6}[/tex].
[tex]\dfrac{5}{6}=\dfrac{-10}{x_2-9}[/tex]
[tex]5(x_2-9)=-10(6)[/tex]
[tex]5x_2-45=-60[/tex]
[tex]5x_2=-60+45[/tex]
[tex]5x_2=-15[/tex]
Divide both sides by 5.
[tex]x_2=-\dfrac{15}{5}[/tex]
[tex]x_2=-3[/tex]
Therefore, the value of [tex]x_2[/tex] is [tex]-3[/tex].
