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, $(x_1, y_1)$ and $(x_2, y_2)$. what is an equivalent equation solved for $y_2$? $y_2 = m(x_2 - x_1) - y_1$ $y_2 = mx_2 - x_1 - y_1$ $y_2 = mx_2 - x_1 + y_1$ $y_2 = m(x_2 - x_1) + y_1$

Explanation:

Step1: Start with the slope formula

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Multiply both sides by \( x_2 - x_1 \)

To isolate \( y_2 - y_1 \), we multiply both sides of the equation by \( x_2 - x_1 \). So we get \( m(x_2 - x_1)=y_2 - y_1 \).

Step3: Add \( y_1 \) to both sides

To solve for \( y_2 \), we add \( y_1 \) to both sides of the equation. This gives us \( y_2=m(x_2 - x_1)+y_1 \).

Answer:

\( y_2 = m(x_2 - x_1)+y_1 \) (the last option among the given choices)