Chapter 13, Problem 8CT

To determine

Write an equation of the line with y-intercept 7 and perpendicular to $y=-2x+3$ .

Answer to Problem 8CT

The equation of the line is $y=2x+7$

Explanation of Solution

Given information :

The line intersects at $\text{(0, 7)}$ and perpendicular to $y=-2x+3$ .

The equation of the perpendicular line = $y=-2x+3$ .

The slope of the perpendicular line, $m_1=-2$

If two lines are perpendicular to each other, then

  $m_1\cdot m_2=-1$

So, $m_2=2$

The equation of the line is $y=m_{2}x+c$

  $y=2x+c$

  $7=2\cdot 0+c$

  $c=7$

Hence,

The equation of the line is $y=2x+7$