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)?

• (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)
• (y_2 = m(x_2 - x_1) - y_1)

Explanation:

State the given formula

Using the Linear Equations knowledge point

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

Clear the denominator

Using the Properties of Equality knowledge point

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

Isolate the target variable

Using the Properties of Equality knowledge point

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

Answer:

• (A) \(y_2 = mx_2 - x_1 + y_1\)
• (B) \(y_2 = mx_2 - x_1 - y_1\)
• (C) \(y_2 = m(x_2 - x_1) + y_1\) (Correct answer)
• (D) \(y_2 = m(x_2 - x_1) - y_1\)