Question

1. what is an equation of a line that passes through the point h and is perpendicular to the line j?

Explanation:

Step1: Find slope of line J

Count rise - over - run. If we assume two points on line J, say $(x_1,y_1)$ and $(x_2,y_2)$, and find $\frac{y_2 - y_1}{x_2 - x_1}$. Let's assume line J has a slope $m_1 = 2$ (by counting grid - squares, for example, if it rises 2 units for every 1 unit run).

Step2: Find slope of perpendicular line

The slope $m_2$ of a line perpendicular to a line with slope $m_1$ is $m_2=-\frac{1}{m_1}$. So if $m_1 = 2$, then $m_2=-\frac{1}{2}$.

Step3: Use point - slope form

The point - slope form of a line is $y - y_0=m(x - x_0)$, where $(x_0,y_0)$ is the point the line passes through. Let the coordinates of point H be $(x_0,y_0)$. Then the equation of the line is $y - y_0=-\frac{1}{2}(x - x_0)$.

Answer:

$y - y_0=-\frac{1}{2}(x - x_0)$ (where $(x_0,y_0)$ are the coordinates of point H)