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1-77.

Use what you learned about the slopes of parallel and perpendicular lines to find the equation of a line that would meet the criteria given below.

1. Find the equation of the line that goes through the point $(0, −3)$ and is perpendicular to the line $y=-\frac{2}{5}x+6$.

• Use the eTool below to help you find the equation in part (a).
Click the link at right for the full version of the eTool: CCG 1-77a HW eTool

Determine the slope of the new line.
Remember that the slope of a perpendicular line is the opposite reciprocal of the slope of the original line.

$m_{\perp} =\frac{5}{2}\ \ \ \ \ \ y=\frac{5}{2}x+y_{\text{int}}$

Substitute in the point given to determine the y-intercept.

$y=\frac{5}{2}x-3$

1. Find the equation of the line that is parallel to the line $−3x+2y=10$ and goes through the point $(0,\ 7)$.

• Use the eTool below to help you find the equation in part (b).
Click the link at right for the full version of the eTool: CCG 1-77b HW eTool

Rewrite the equation in $y=mx+b$ form. What is the slope of a parallel line?

$y=\frac{3}{2}x+7$