Question

consider the formula for the slope between two coordinate points, \\(m\\), shown below.
\\m = \frac{y_2 - y_1}{x_2 - x_1}\\
which of the following equations is equivalent to the slope formula?

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

Explanation:

Multiply both sides by the denominator

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

Isolate \(y_2\) by adding \(y_1\) to both sides

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

Match with the given options

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

Answer:

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