Question

On a coordinate plane, a line goes through (negative 4, 4) and (4, negative 2). A point is at (6, 0).
What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

y = –Three-fourthsx + 8
y = –Three-fourthsx + 6
y = Four-thirdsx – 8
y = Four-thirdsx – 6

Answer 1

To find the equation of the line that is perpendicular to the given line and has an x-intercept of 6, we can follow these steps:

1. **Find the slope of the given line**:
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-4, 4)\) and \((4, -2)\):

\[
m = \frac{-2 - 4}{4 - (-4)} = \frac{-6}{8} = -\frac{3}{4}
\]

2. **Find the slope of the line that is perpendicular**:
The slope of a line that is perpendicular to another is the negative reciprocal of the slope of the original line. Therefore, if the slope of the original line is \(-\frac{3}{4}\), the slope of the perpendicular line \( m_{\perpendicular} \) is:

\[
m_{\perpendicular} = \frac{4}{3}
\]

3. **Use the x-intercept to find the equation**:
The x-intercept is the point where the line crosses the x-axis, which occurs when \( y = 0 \). For our line,