question graph the line passing through the point (-1, -3) whose slope is m = 4, by plotting the slope and…

Explanation:

Step1: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-1,-3)$ and $m = 4$. So $y+3 = 4(x + 1)$.

Step2: Convert to slope - intercept form

Expand the right - hand side: $y+3=4x + 4$. Then solve for $y$: $y=4x+1$.

Step3: Find the y - intercept

In the slope - intercept form $y = mx + b$ ($m$ is slope and $b$ is y - intercept), for $y=4x + 1$, the y - intercept is $(0,1)$.

Step4: Use the slope to find another point

The slope $m = 4=\frac{\Delta y}{\Delta x}$. Starting from the point $(0,1)$, if $\Delta x = 1$, then $\Delta y=4$. So another point is $(0 + 1,1+4)=(1,5)$. Plot the points $(-1,-3)$, $(0,1)$ and $(1,5)$ and draw a line through them.

Answer:

The line is graphed by plotting the point $(-1,-3)$, the y - intercept $(0,1)$ and using the slope to find additional points like $(1,5)$ and drawing a straight line through them.