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 the slope formula

We have the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). To solve for \( y_2 \), first multiply both sides by \( x_2 - x_1 \) to eliminate the denominator.
\( m(x_2 - x_1) = y_2 - y_1 \)

Step2: Isolate \( y_2 \)

Add \( y_1 \) to both sides of the equation to solve for \( y_2 \).
\( y_2 = m(x_2 - x_1) + y_1 \)

Answer:

\( y_2 = m(x_2 - x_1) + y_1 \) (corresponding to the option \( y_2 = m(x_2 - x_1) + y_1 \))