Question

Find the equation:

a. of a line parallel to the given line and through the indicated y-intercept.

b. of a line perpendicular to the given line and through the indicated y-intercept.11. Table of a line:

y

3/-8

4/-10

5/-12

6/-14

Answer 1

To find the equations of a line parallel and perpendicular to the given line, we first need to find the slope of the line represented by the given table.

The table provides the following points:

- \((3, -8)\)
- \((4, -10)\)
- \((5, -12)\)
- \((6, -14)\)

To determine the slope \(m\), we can use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((3, -8)\) and \((4, -10)\):
\[
m = \frac{-10 - (-8)}{4 - 3} = \frac{-10 + 8}{1} = \frac{-2}{1} = -2
\]

So, the slope of the line represented by the table is \(m = -2\).

### a. Equation of a Line Parallel to the Given Line

A line parallel to the given line will have the same slope, which is \(-2\). We need to use this slope and the indicated y-intercept to write the equation.

Let's say the indicated y-intercept is \(b\). The equation of the line in slope-intercept form \(y = mx + b\) will be:

\[
y = -2x + b
\]

**(Please provide the indicated y-intercept if you want a specific equation.)**

### b. Equation of a Line Perpendicular to the Given Line

The slope of a line that is perpendicular to another is the negative reciprocal of the slope of the original line.

Given the slope of the original line is \(-2\), the slope of the perpendicular line will be:
\[
m_{\text{perpendicular}} = -\frac{1}{-2} = \frac{1}{2}
\]

Again, let's assume the indicated y-intercept for the perpendicular line is \(b'\). Then the equation of the line will be:

\[
y = \frac{1}{2}x + b'
\]

**(Please provide the indicated y-intercept if you want a specific equation.)**

In summary, we need the y-intercepts to provide specific equations. If you provide \(b\) and \(b'\), I can finalize those equations for you.