Question

the graph of a line is shown on the coordinate grid. what is the equation of the line perpendicular to the graphed line going through the point (0, 2)? y = -3x + 2 y = -\frac{1}{3}x + 2 y = \frac{1}{3}x + 2 y = 3x + 2

Explanation:

Step1: Find slope of given line

Pick two points on the line, say $(0, 2)$ and $(6, 0)$. The slope $m_1$ of the given line using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ is $m_1=\frac{0 - 2}{6-0}=-\frac{1}{3}$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_2$. Then $m_1\times m_2=-1$. Substituting $m_1 =-\frac{1}{3}$, we get $-\frac{1}{3}\times m_2=-1$, so $m_2 = 3$.

Step3: Use point - slope form

The line passes through the point $(0,2)$ and has slope $m_2 = 3$. The point - slope form of a line is $y - y_1=m(x - x_1)$. Here $x_1 = 0,y_1 = 2,m = 3$. Substituting these values, we get $y-2=3(x - 0)$, which simplifies to $y=3x + 2$.

Answer:

$y = 3x+2$