Question

graph the line with the equation $y = -\frac{1}{3}x + 4$.

Explanation:

Step1: Identify y-intercept

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

Step2: Identify slope

The slope $m=-\frac{1}{3}$, meaning $\frac{\text{change in } y}{\text{change in } x}=-\frac{1}{3}$. For every 3 units right in $x$, $y$ decreases by 1.

Step3: Find a second point

Starting from $(0,4)$, move 3 units right to $x=3$, then 1 unit down to $y=3$. This gives the point $(3, 3)$.

Step4: Draw the line

Plot points $(0,4)$ and $(3,3)$, then draw a straight line through them, extending it across the grid.

Answer:

The line passes through points $(0, 4)$ and $(3, 3)$ (and other points following the slope $-\frac{1}{3}$), forming a downward-sloping line on the coordinate plane.