Question

graph this line using the slope and y-intercept:
$y = \frac{1}{2}x - 4$
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b$ is the y-intercept. For $y=\frac{1}{2}x - 4$, $b=-4$. So the y-intercept point is $(0, -4)$.

Step2: Identify slope

In $y=mx+b$, $m$ is the slope. Here, $m=\frac{1}{2}$, meaning $\frac{\text{rise}}{\text{run}}=\frac{1}{2}$.

Step3: Find second point

From $(0, -4)$, move up 1 unit and right 2 units. This gives the point $(0+2, -4+1)=(2, -3)$.

Step4: Draw the line

Connect the points $(0, -4)$ and $(2, -3)$, then extend the line across the grid.

Answer:

The line passes through points such as $(0, -4)$ and $(2, -3)$, and extends infinitely in both directions across the coordinate grid.