- Class: CPI Precalculus
- Author: Peter Atlas
- Text:
__Advanced Mathematics__, Brown

- Find an equation for the line described:
- passes through (-3, -1) and has a slope 4.
- passes through \( \displaystyle \left( \frac{5}{2}, 0 \right) \) and has a slope \( \displaystyle \frac{1}{2}.\)
- has x-intercept 6 and y-intercept 5
- has x-intercept -2 and slope \( \displaystyle \frac{3}{4}.\)
- passes through (1, 2) and (2, 6).
- passes through (-7, -2) and (0, 0).
- passes through (-3, 4) and is parallel to the x-axis.
- passes through (-3, 4) and is parallel to the y-axis.

## Solution

\( y + 1 = 4(x + 3) \)## Solution

\( \displaystyle y = \frac{1}{2} \left( x - \frac{5}{2} \right) \)## Solution

\( \displaystyle \frac{x}{6} + \frac{y}{5} = 1 \)## Solution

\( \displaystyle y + 2 = \frac{3}{4}x \)## Solution

\( y - 2 = 4(x - 1) \)## Solution

\( \displaystyle y = \frac{2x}{7} \)## Solution

\( y = 4 \)## Solution

\( x = -3 \) - Determine whether each pair of lines is parallel, perpendicular, or neither
- \(3x - 4y = 12\) and \(4x - 3y = 12\)
- \(y = 5x - 16\) and \( y = 5x + 2\)
- \( 5x - 6y = 25\) and \( 6x + 5y = 0\)
- \(x = 8y + 3\) and \( \displaystyle 4y - \frac{x}{2} = 32\)

## Solution

Neither## Solution

Parallel## Solution

Perpendicular## Solution

Parallel - Find the equation of the line described. Write your \( ANSWER \) in standard form:
- is parallel to \(2x - 5y = 10\) and passes through (-1, 2).
- is perpendicular to \(4y - 3x = 1\) and passes through (4, 0).
- is perpendicular to \(x - y + 2 = 0\) and passes through (3, 1).
- is parallel to \(3x - 5y = 25\) and has the same y-intercept as the line \(6x - y + 11 = 0\).

## Solution

\( 2x - 5y = -12 \)## Solution

\( 4x + 3y = 16 \)## Solution

\( x + y = 4 \)## Solution

\( 3x - 5y = -55 \) - Find the slope of the line passing through the two points (3, 9) and \( (3 + h, (3 + h)^2)\).
- Find the slope of the line passing through the two points \( (x, x^2) \) and \( (x + h, (x + h)^2) \).
- Find the linear function satisfying the given conditions :
- \(f(-1) = 0\) and \(f(5) = 4\).
- f(3) = 2 and f(-3) = -4
- \(g(0) = 0\) and \(g(1) = \sqrt{2}.\)
- The graph passes through the points (2, 4) and (3, 9).
- \( \displaystyle f \left( \frac{1}{2} \right) = -3\), and the graph of \(f\) is a line parallel to the line \(x - y = 1\).
- \(g(2) = 1\) and the graph of \(g\) is perpendicular to the line \(6x - 3y = 2\)

## Solution

\( \displaystyle y = \frac{2}{3}(x + 1) \)## Solution

\( y - 2 = x - 3 \)## Solution

\( y = \sqrt{2}x \)## Solution

\( y - 4 = 5(x - 2) \)## Solution

\( \displaystyle y + 3 = x - \frac{1}{2} \)## Solution

\( \displaystyle y - 1 = -\frac{1}{2}(x - 2) \)