Question

Write the point-slope form of the equation of the line that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form. $$ (4,-2), m=\frac{1}{4} $$

Short answer

The equation of the line in point-slope form is \(y + 2 = \frac{1}{4}x - 1\) and in slope-intercept form it is \(y = \frac{1}{4}x - 3\).

Step-by-step solution

Writing the Equation in Point-Slope Form

Given the point (4,-2) and slope \(m=\frac{1}{4}\), let's substitute these values into the point-slope form equation. So we get \(y - (-2) = \frac{1}{4} (x - 4)\).

Simplifying the Equation

Simplify the equation by removing the parenthesis and reducing any possible terms. So the equation becomes \(y + 2 = \frac{1}{4}x - 1\).

Rewrite the Equation in Slope-Intercept Form

To transform the equation to slope-intercept form \(y = mx + c\), we just need to isolate \(y\) on one side. Subtract 2 from both sides to get \(y = \frac{1}{4}x - 3\).