Question

1. $y = -\frac{1}{2}x - 3$ $m = -\frac{1}{2}, b=(-3)$ $(0, - 3)$

Explanation:

Step1: Identify the y - intercept

The equation is in slope - intercept form $y = mx + b$, where $b$ is the y - intercept. Here $b=-3$, so the line crosses the y - axis at the point $(0, - 3)$. Plot the point $(0,-3)$ on the graph.

Step2: Use the slope to find another point

The slope $m =-\frac{1}{2}$. The slope is $\frac{\text{rise}}{\text{run}}$. So from the point $(0,-3)$, since the rise is $- 1$ (down 1 unit) and the run is 2 (right 2 units), we can find another point. Starting from $(0,-3)$, moving down 1 unit and right 2 units gives the point $(2,-4)$.

Step3: Draw the line

Connect the points $(0,-3)$ and $(2,-4)$ with a straight line. This line represents the graph of the equation $y =-\frac{1}{2}x - 3$.

Answer:

The graph of the line $y =-\frac{1}{2}x - 3$ is drawn by plotting the y - intercept $(0,-3)$ and using the slope $-\frac{1}{2}$ to find another point $(2,-4)$ and then connecting the two points.