Problem 33 - 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 \((-3,-1)\) and \((4,-1)\)

Step-by-Step Solution

Answer

The point-slope form of the line is \(y = -1\) and the slope-intercept form of the line is also \(y = -1\).

Step 1: Find the Slope

The slope of the line (m) can be calculated using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the given points into this formula gives \(m = \frac{-1 - (-1)}{4 - (-3)} = \frac{0}{7} = 0\). Thus, the slope of the line is 0.

Step 2: Write the Point-Slope Form

The point-slope form of the line equation is given by \(y - y_1 = m(x - x_1)\). Substituting point (-3,-1) and the slope yields \(y - (-1) = 0(x - (-3))\), which simplifies to \(y + 1 = 0 \Rightarrow y = -1\).

Step 3: Write the Slope-Intercept Form

The slope-intercept form of the line equation is \(y = mx + b\), where b is the y-intercept. Since the slope is 0 and the line is horizontal, it crosses the y-axis at y = -1. Therefore, the slope-intercept form of the line is \(y = 0x - 1 \Rightarrow y = -1\).