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Answer:
[tex]y - 3 = \frac{2}{7} ( x - 8)[/tex]
Step-by-step explanation:
We are given that a line passes through the points (8, 3) and (-6, -1). We want to write the equation of this line in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
First, we need to find the slope of the line.
The equation for finding the slope from two points is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1 ,y_1)[/tex] and [tex](x_2 ,y_2)[/tex] are points.
We can label the values of the points beforehand:
[tex]x_1 = 8 \\y_1=3\\x_2=-6\\y_2=-1[/tex]
Now, substitute into the equation.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-1-3}{-6-8}[/tex]
[tex]m=\frac{-4}{-14}[/tex]
[tex]m=\frac{2}{7}[/tex]
Now, substitute the values given (m and [tex](x_ 1, y_1)[/tex] into the equation in point-slope form):
[tex]y - 3 = \frac{2}{7} ( x - 8)[/tex]