Problem 30 - College Algebra Essentials

Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-4)\) and \((1,-1)\)

Step-by-Step Solution

Answer

The point-slope form of the line is \(y + 4 = x + 2\), and the slope-intercept form is \(y = x - 2\).

Step 1: Find the slope

First, calculate the slope (m) of the line using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). In this case, we have two points \((-2,-4)\) and \((1,-1)\), so we can substitute these into the formula to get \(m =\frac{-1 - (-4)}{1 - (-2)}\). After doing the calculation we find that \(m = 1\)

Step 2: Write the point-slope form

The point-slope formula is \(y - y_1 = m(x - x_1)\). Substituting the point \((-2,-4)\) and the slope \(m = 1\) into the formula, we get \(y - (-4) = 1(x - (-2))\). Simplify to obtain \(y + 4 = x + 2\)

Step 3: Write the slope-intercept form

The slope-intercept formula is \(y = mx + b\), where \(b\) is the y-intercept. First, rearrange the point-slope equation from Step 2 into the slope-intercept form, yielding \(y = x - 2\).