Question

find the equation of the line that contains the point (4, - 2) and is perpendicular to the line y=-2x + 5.
○ y=-2x + 6
○ y=-\frac{1}{2}x
○ y=2x - 10
○ y=\frac{1}{2}x-4

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the line $y = - 2x+5$ is $m_1=-2$. If two lines are perpendicular, the product of their slopes $m_1\times m_2=- 1$. So, $-2\times m_2=-1$, then $m_2=\frac{1}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(4,-2)$ and $m = \frac{1}{2}$. Substitute these values: $y-(-2)=\frac{1}{2}(x - 4)$.

Step3: Simplify the equation

$y + 2=\frac{1}{2}x-2$. Then $y=\frac{1}{2}x-4$.

Answer:

$y=\frac{1}{2}x - 4$