Answer:
[tex]y - 3 = -10 (x-2)[/tex]
Step-by-step explanation:
The point-slope formula is [tex]y-y_1 = m (x-x_1)[/tex]. When knowing the slope of a line and a point it intersects, we can write its equation with that formula. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
1) First, find [tex]m[/tex], or the slope. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the x and y values of the given points. Then, solve:
[tex]m = \frac{(-7)-(3)}{(3)-(2)} \\m = \frac{-7-3}{3-2} \\m = \frac{-10}{1} \\m = -10[/tex]
Therefore, the slope of the line is -10.
2) Now, substitute the needed real values into the point-slope formula, [tex]y-y_1 = m (x-x_1)[/tex]. Since [tex]m[/tex] represents the slope, substitute -10 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line crosses, choose any of the points given and substitute its values into the formula. (Either one is fine, they both equal the same thing. I chose (2,3).) This will give the following answer and equation:
[tex]y - 3 = -10 (x-2)[/tex]
