Question

1. create a graph of the equation y = \frac{1}{2}x - 3.

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form $y = mx + b$, where $b$ is the y - intercept. For $y=\frac{1}{2}x - 3$, when $x = 0$, $y=-3$. So the point $(0,-3)$ is on the line.

Step2: Find another point using the slope

The slope $m=\frac{1}{2}$. Starting from the y - intercept $(0,-3)$, using the slope formula $\text{slope}=\frac{\Delta y}{\Delta x}$. If $\Delta x = 2$, then $\Delta y=1$. So another point is $(0 + 2,-3+1)=(2,-2)$.

Step3: Plot the points and draw the line

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

Answer:

Graph with a line passing through points $(0,-3)$ and $(2,-2)$ on the given coordinate grid.