Question

The slope, m, of a linear equation can be found using the formula m = StartFraction y 2 minus y a Over x 2 minus x 1 EndFraction., where the x- and y-values come from two ordered pairs, and (x1, y1) and (x2, y2).
What is an equivalent equation solved for y2?

y2 = mx2 – x1 + y1
y2 = mx2 – x1 – y1
y2 = m(x2 – x1) + y1
y2 = m(x2 – x1) – y1

Answer 1

Answer: Third option.

Step-by-step explanation:

By definition, the slope of a line can be calculated with the following formula:

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

Since you need to solve for $y_2$ to find an equivalent expression, you can apply these steps:

1. You must multiply both sides of the equation by $(x_2-x_1)$:

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

2. Finally, you must add $y_1$ to both sides of the equation:

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

Answer 2

Answer:

C.y2 = m(x2 – x1) + y1

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