Questions: Find the equation of the line passing through the points (-4,8) and (2,-7). Write the equation in point-slope form.

Transcript text: Find the equation of the line passing through the points $(-4,8)$ and $(2,-7)$. Write the equation in point-slope form.

Solution

Step 1: Calculate the Slope

The slope $m$ is calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - 8}{2 + 4} = -2.5$.

Step 2: Use the Point-Slope Form

Using the point-slope form $y - y_1 = m(x - x_1)$ with $(x_1, y_1) = (-4, 8)$ and $m = -2.5$, we get $y - 8 = -2.5(x + 4)$.

Step 3: Solve for y to Get the Slope-Intercept Form

Solving for $y$, we get $y = -2.5x - 2$.

The equation of the line in slope-intercept form is $y = -2.5x - 2$.

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