Question

which equation represents a line which is perpendicular to the line y - 2x = 3? answer attempt 1 out of 2 y = 1/2x - 6 y = 2x - 1 y = -1/2x + 7 y = -2x + 4

Explanation:

Step1: Transform the given line to slope - intercept form

Transform $y - 2x=3$ to $y = 2x + 3$, its slope $m_1 = 2$.

Step2: Determine the slope of the perpendicular line

For two perpendicular lines with slopes $m_1$ and $m_2$, $m_1\times m_2=- 1$. Given $m_1 = 2$, then $2\times m_2=-1$, so $m_2=-\frac{1}{2}$.

Step3: Find the correct equation

The equation of a line in slope - intercept form is $y = m_2x + b$. The line with slope $m_2 =-\frac{1}{2}$ is $y=-\frac{1}{2}x + 7$.

Answer:

$y =-\frac{1}{2}x + 7$