Question

complete the following equations.
enter an equation for line j: y = x

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For a line passing through the origin ($b = 0$), the equation is $y=mx$.

Step2: Identify two points on the line

The line passes through the origin $(0,0)$ and another point, say $(2, - 10)$.

Step3: Calculate the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(2,-10)$, we have $m=\frac{-10 - 0}{2 - 0}=\frac{-10}{2}=-5$.

Answer:

$-5$