Answer:
[tex]y -5 = \frac{9}{13}(x - 7)[/tex]
Step-by-step explanation:
Given :
Two points are given in graph (-6, -4) and {7, 5).
The point-slope form of the equation of a straight line is:
[tex]y -y_{1} = m(x - x_{1})[/tex]------------(1)
Let [tex](x_{1}, y_{1})=(7,5)[/tex] and [tex](x_{2}, y_{2})=(-6,-4)[/tex]
The slope of the line [tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
Put all known value in above equation.
[tex]m=\frac{-4- 5}{-6- 7}[/tex]
[tex]m=\frac{-9}{-13}[/tex]
[tex]m=\frac{9}{13}[/tex]
The slope of the line [tex]m=\frac{9}{13}[/tex]
We know m, and also know that [tex](x_{1}, y_{1})=(7,5)[/tex], so we put these value in equation 1.
[tex]y -5 = \frac{9}{13}(x - 7)[/tex]
Therefore, the equation of the line is [tex]y -5 = \frac{9}{13}(x - 7)[/tex].
