Question: Find the equation of the line passing through the given pair of points. Write the equation in…

Find the equation of the line passing through the given pair of points. Write the equation in slope-intercept form.

\((-4, -2), (5, 6)\)

What is the slope-intercept form of the equation that passes through \((-4, -2)\) and \((5, 6)\)?

(Simplify your answer. Type your answer in slope-intercept form.)

Solution

To find the equation of the line passing through the points \((-4, -2)\) and \((5, 6)\) in slope-intercept form \(y = mx + b\), follow these steps: First, find the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the given points \((x_1, y_1) = (-4, -2)\) and \((x_2, y_2) = (5, 6)\): \[ m = \frac{6 - (-2)}{5 - (-4)} \] \[ m = \frac{6 + 2}{5 + 4} \] \[ m = \frac{8}{9} \] Now use the slope-intercept form equation \(y = mx + b\) with one of the points to solve for \(b\). Let’s use the point \((-4, -2)\): \[ -2 = \frac{8}{9}(-4) + b \] \[ -2 = -\frac{32}{9} + b \] Add \(\frac{32}{9}\) to both sides to solve for \(b\): \[ b = -2 + \frac{32}{9} \] Convert \(-2\) to a fraction with a denominator of 9: \[ -2 = -\frac{18}{9} \] \[ b = -\frac{18}{9} + \frac{32}{9} \] \[ b = \frac{14}{9} \] So, the equation in slope-intercept form is: \[ y = \frac{8}{9}x + \frac{14}{9} \]