Question: Find the equation of this line. \[ y = \frac{?}{x} + \boxed{?} \] Simplify your answer…

Find the equation of this line.

\[ y = \frac{?}{x} + \boxed{?} \]

Simplify your answer completely.

Solution

Step 1: Find the slope \( m \) using the two points. \[ m = \frac{3 - (-2)}{5 - (-2)} = \frac{5}{7} \] Step 2: Use the slope and one point to find the y-intercept \( b \). \[ 3 = \frac{5}{7} \times 5 + b \] \[ 3 = \frac{25}{7} + b \] \[ b = 3 - \frac{25}{7} = -\frac{4}{7} \] Step 3: Write the equation of the line. \[ y = \frac{5}{7}x - \frac{4}{7} \]