Question

find the equation of a line perpendicular to $y = -\frac{1}{2}x + 9$ that passes through the point $(1,7)$. answer $y + 7 = -\frac{1}{2}(x + 1)$ $y - 7 = \frac{1}{2}(x - 1)$ $y - 7 = 2(x - 1)$ $y - 7 = 2(x + 1)$

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line $y = -\frac{1}{2}x + 9$ is $m_1=-\frac{1}{2}$. If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_2$. Then $m_1\times m_2=-1$. So, $-\frac{1}{2}\times m_2=-1$, and $m_2 = 2$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(1,7)$ and $m = 2$. Substituting these values into the point - slope form, we get $y - 7=2(x - 1)$.

Answer:

$y - 7=2(x - 1)$