Question

graph the line with the equation $y = -\frac{1}{2}x - 4$.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=-4$. So the y-intercept is the point $(0, -4)$.

Step2: Identify slope

The slope $m=-\frac{1}{2}$, meaning for every 2 units right ($\Delta x=2$), y decreases by 1 ($\Delta y=-1$).

Step3: Find second point

Start from $(0, -4)$, move 2 right and 1 down: $(0+2, -4-1)=(2, -5)$.

Step4: Draw the line

Plot points $(0, -4)$ and $(2, -5)$, then draw a straight line through them (extend it across the grid).

Answer:

The line passes through points such as $(0, -4)$ and $(2, -5)$, extending infinitely in both directions on the coordinate plane.