Question

graph the line.
$y=3x+1$

Explanation:

Step1: Identify slope and y-intercept

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

Step2: Plot the y-intercept

Mark the point $(0,1)$ on the coordinate grid.

Step3: Use slope to find a second point

Slope $m=3=\frac{3}{1}$, meaning for every 1 unit right in $x$, move 3 units up in $y$. From $(0,1)$, move 1 right to $x=1$, then 3 up to $y=4$. This gives the point $(1,4)$. Mark this point.

Step4: Draw the line

Connect the points $(0,1)$ and $(1,4)$ with a straight line, extending it across the grid.

Answer:

The line $y=3x+1$ is graphed by plotting the y-intercept $(0,1)$, using the slope to find a second point $(1,4)$, then drawing a straight line through these points (extending across the provided grid).