Answer:
The equation in point-slope form of the line is:
[tex]y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)[/tex]
Step-by-step explanation:
Given the points
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-1,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:2\right)[/tex]
[tex]m=\frac{2-\left(-5\right)}{3-\left(-1\right)}[/tex]
[tex]m=\frac{7}{4}[/tex]
As the point-slope form is defined as
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope.
substituting the values m=7/4 and the first point (-1, -5)
[tex]y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)[/tex]
Therefore, the equation in point-slope form of the line is:
[tex]y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)[/tex]
