Question

Write the equation of the line that passes through the points (2, 3) and (3, -7). Put

Answer 1

Answer:

$y - 3 = -10 (x-2)$

Step-by-step explanation:

The point-slope formula is $y-y_1 = m (x-x_1)$. When knowing the slope of a line and a point it intersects, we can write its equation with that formula. Substitute $m$, $x_1$, and $y_1$ for real values.

1) First, find $m$, or the slope. Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$ and substitute the x and y values of the given points. Then, solve:

$m = \frac{(-7)-(3)}{(3)-(2)} \\m = \frac{-7-3}{3-2} \\m = \frac{-10}{1} \\m = -10$

Therefore, the slope of the line is -10.

2) Now, substitute the needed real values into the point-slope formula, $y-y_1 = m (x-x_1)$. Since $m$ represents the slope, substitute -10 in its place. Since $x_1$ and $y_1$ 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:

$y - 3 = -10 (x-2)$