Question

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

Explanation:

Step1: Identify slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $y=-\frac{1}{2}x - 3$, we have $m =-\frac{1}{2}$ and $b=-3$.

Step2: Plot y - intercept

The y - intercept is the point where the line crosses the y - axis. Since $b = - 3$, the line crosses the y - axis at the point $(0,-3)$. Plot this point on the graph.

Step3: Use slope to find another point

The slope $m=-\frac{1}{2}=\frac{\text{rise}}{\text{run}}$. From the point $(0,-3)$, for a run of 2 (move 2 units to the right along the x - axis), the rise is - 1 (move 1 unit down along the y - axis). So we get the point $(2,-4)$.

Step4: Draw the line

Connect the points $(0,-3)$ and $(2,-4)$ with a straight line, which extends infinitely in both directions.

Answer:

The graph of the line $y =-\frac{1}{2}x - 3$ is drawn as shown in the provided image, with a y - intercept of $(0,-3)$ and a slope of $-\frac{1}{2}$.