Question

using the slope and y-intercept:
$y = 3x + 1$
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 $y=3x+1$, $b=1$, so the y-intercept point is $(0, 1)$.

Step2: Use slope to find second point

Slope $m=3=\frac{3}{1}$, meaning rise 3, run 1. From $(0,1)$, add 1 to $x$ and 3 to $y$: $(0+1, 1+3)=(1,4)$.

Step3: Plot and connect points

Mark $(0,1)$ and $(1,4)$, then draw a straight line through them extending across the grid.

Answer:

The line passes through points $(0, 1)$ and $(1, 4)$ (and other points following the slope, e.g., $(2,7)$, $(3,10)$), forming a straight line with slope 3 and y-intercept 1.