Question

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

Explanation:

Step1: Identify the y - intercept

The equation of the line 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 $(0, - 3)$.

Step2: Identify the slope

The slope $m =-\frac{1}{2}$. This means for every 2 units we move to the right along the x - axis, we move 1 unit down along the y - axis. Starting from the y - intercept $(0,-3)$, if we move 2 units to the right (x = 2), then $y=-\frac{1}{2}(2)-3=-1 - 3=-4$, giving the point $(2,-4)$. If we move 2 units to the left of the y - intercept (x=-2), then $y =-\frac{1}{2}(-2)-3=1 - 3=-2$, giving the point $(-2,-2)$.

Step3: Plot the points and draw the line

Plot the points $(0,-3)$, $(2,-4)$ and $(-2,-2)$ on the coordinate grid and draw a straight line passing through them.

Answer:

The line $y =-\frac{1}{2}x - 3$ is plotted on the coordinate grid using the y - intercept $(0,-3)$ and the slope $-\frac{1}{2}$ to find additional points.