3 What are the slope and \( y \)-intercept of the line that passes through the pair of points \( (5,1) \) and \( (-10,-11) \) ?
(A) \( m=-3, b=\frac{4}{5} \)
(B) \( m=\frac{4}{5}, b=-3 \)
\( m=3, b=-\frac{4}{5} \)
(D) \( m=-\frac{4}{5}, b=3 \)

Answer

Expert–verified

Hide Steps

Answer

Step 3: Convert to slope-intercept form: y = -\(\frac{4}{5}\)x + \(\frac{4}{5}\)(5) + 1

Steps

Step 1 ：Step 1: Calculate the slope: m = \(\frac{y_2 - y_1}{x_2 - x_1}\) = \(\frac{-11 - 1}{-10 - 5}\) = \(\frac{-12}{15}\) = \(-\frac{4}{5}\)

Step 2 ：Step 2: Use point-slope form: y - 1 = -\(\frac{4}{5}\)(x - 5)

Step 3 ：Step 3: Convert to slope-intercept form: y = -\(\frac{4}{5}\)x + \(\frac{4}{5}\)(5) + 1