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: 1-77a HW eTool

  Step 1(a):

  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.

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

  Step 2(a):

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

  Answer(a):

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

2. 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: 1-77b HW eTool

  Hint(b):

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

  Answer (b):

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