Question

question graph the line passing through the point (-1, -3) whose slope is m = 4, by plotting the slope and the intercept. provide your answer below:

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 subtract 3 from both sides to get $y=4x+1$.

Step3: Identify y - intercept

In the equation $y = 4x + 1$, the y - intercept is $b = 1$, so the line crosses the y - axis at the point $(0,1)$.

Step4: Use 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 ($\Delta x=1$), we move 4 units up ($\Delta y = 4$), getting the point $(1,5)$. Plot the points $(-1,-3)$, $(0,1)$ and $(1,5)$ and draw a line through them.

Answer:

The line is graphed by first using the point - slope form to get the slope - intercept form $y = 4x+1$, identifying the y - intercept $(0,1)$, using the slope to find additional points, and then drawing a line through the points. (The graph is already provided in the problem statement and the above steps explain the process of graphing it).