Problem 20 - College Algebra Essentials

Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(=-1,\) passing through \(\left(-4,-\frac{1}{4}\right)\)

Step-by-Step Solution

Answer

The point-slope form of the line is \(y - (-\frac{1}{4}) = -1 (x - (-4))\), and the slope-intercept form is \(y = -x - \frac{17}{4}\).

Step 1: Find the Point-Slope form

Plug the given values into the point-slope formula: \(y + \frac{1}{4} = -1(x + 4)\). We can simplify this to \(y + \frac{1}{4} = -x - 4\). So, the point-slope form of the line is \(y - (-\frac{1}{4}) = -1(x -(-4))\).

Step 2: Convert to Slope-Intercept form

To convert the equation from point-slope form to slope-intercept form, we isolate \(y\). Doing so, we obtain \(y = -x - 4 - \frac{1}{4}\). Simplifying, we get \(y = -x - \frac{17}{4}\). Hence, the slope-intercept form of the line is \(y = -x - \frac{17}{4}\).