Question

1. $y = -3x$

Explanation:

Step1: Identify slope and intercept

The equation $y=-3x$ is in slope-intercept form $y=mx+b$, where $m=-3$ (slope) and $b=0$ (y-intercept).

Step2: Plot y-intercept

The y-intercept is $(0,0)$, so mark this point on the origin of the coordinate plane.

Step3: Use slope to find next point

Slope $m=\frac{\Delta y}{\Delta x}=\frac{-3}{1}$. From $(0,0)$, move 1 unit right and 3 units down to get the point $(1,-3)$; or move 1 unit left and 3 units up to get $(-1,3)$.

Step4: Draw the line

Connect the points $(0,0)$, $(1,-3)$, and $(-1,3)$ with a straight line, extending it in both directions as shown in the graph.

Answer:

The graph of $y=-3x$ is a straight line passing through the origin $(0,0)$, with a slope of $-3$, passing through points like $(1,-3)$ and $(-1,3)$, extending infinitely in both directions as depicted.