Question

graph the line with the equation
$y = \frac{1}{6}x + 4$.

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: Use slope to find second point

Slope $m=\frac{1}{6}$, meaning $\frac{\text{rise}}{\text{run}}=\frac{1}{6}$. From $(0,4)$, move 6 units right and 1 unit up to get the point $(6, 5)$.

Step3: Plot and connect points

Mark $(0,4)$ and $(6,5)$ on the grid, then draw a straight line through them (extending it across the graph).

Answer:

The line passes through points $(0, 4)$ and $(6, 5)$, and extends infinitely in both directions across the coordinate grid.