Question

select the correct answer.
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?
\\(\bigcirc\\) a. $x_2 = m(y_2 - y_1) + x_1$
\\(\bigcirc\\) b. $y_2 = m(x_2 - x_1) + y_1$
\\(\bigcirc\\) c. $y_1 = m(x_2 - x_1) + y_2$
\\(\bigcirc\\) d. $x_1 = m(y_2 - y_1) + x_2$

Explanation:

Step1: Start with the slope formula

We have the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

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

To eliminate the denominator, we multiply both sides of the equation by \( x_2 - x_1 \). This gives us \( m(x_2 - x_1) = y_2 - y_1 \).

Step3: Add \( y_1 \) to both sides

Now, we add \( y_1 \) to both sides of the equation to solve for \( y_2 \). So, \( m(x_2 - x_1) + y_1 = y_2 \), which can be rewritten as \( y_2 = m(x_2 - x_1) + y_1 \).

Answer:

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