Question

the slope, m, of a linear equation can be found using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where the x- and y-values come from two ordered pairs, and $(x_1, y_1)$ and $(x_2, y_2)$. what is an equivalent equation solved for $y_2$? $\bigcirc$ $y_2 = mx_2 - x_1 + y_1$ $\bigcirc$ $y_2 = mx_2 - x_1 - y_1$ $\bigcirc$ $y_2 = m(x_2 - x_1) + y_1$ $\bigcirc$ $y_2 = m(x_2 - x_1) - y_1$

Explanation:

Step1: Start with slope formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Multiply both sides by $x_2-x_1$

$m(x_2 - x_1) = y_2 - y_1$

Step3: Isolate $y_2$ by adding $y_1$

$y_2 = m(x_2 - x_1) + y_1$

Answer:

$y_2 = m(x_2 - x_1) + y_1$ (the third option)