Question

graph the line with y - intercept 1 and slope 4.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m = 4$ and $b = 1$, the equation of the line is $y=4x + 1$.

Step2: Find the y - intercept point

The y - intercept is 1, so the line passes through the point $(0,1)$. Plot this point on the coordinate plane.

Step3: Use the slope to find another point

The slope $m = 4=\frac{\Delta y}{\Delta x}$. Starting from the point $(0,1)$, if we move 1 unit to the right ($\Delta x = 1$), then $\Delta y=4$. So we get to the point $(1,5)$. Plot this point.

Step4: Draw the line

Connect the two points $(0,1)$ and $(1,5)$ with a straight - line and extend it in both directions.

Answer:

Graph the line passing through the points $(0,1)$ and $(1,5)$ and extending infinitely in both directions.