graph the line.\ny = 3x + 1

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form $y = mx + b$, where $b$ is the y - intercept. For $y=3x + 1$, when $x = 0$, $y=1$. So the y - intercept is the point $(0,1)$.

Step2: Find the slope and another point

The slope $m = 3=\frac{\text{rise}}{\text{run}}$. Starting from the y - intercept $(0,1)$, since the slope is 3, for a run of 1 (increase $x$ by 1), the rise is 3 (increase $y$ by 3). So another point is $(1,4)$.

Step3: Draw the line

Plot the points $(0,1)$ and $(1,4)$ on the coordinate plane and draw a straight line passing through them.

Answer:

Graph the line by plotting the points $(0,1)$ and $(1,4)$ and drawing a straight - line through them.