Question

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

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: Plot the $y$-intercept

The $y$-intercept is $-1$, so we plot the point $(0,-1)$ on the $y$-axis.

Step3: Use the slope to find another point

The slope $m=-4=\frac{-4}{1}=\frac{\text{rise}}{\text{run}}$. Starting from the point $(0,-1)$, we move down 4 units (because the rise is - 4) and then 1 unit to the right (because the run is 1). This gives us the point $(1,-5)$. We can also move up 4 units and 1 unit to the left from $(0,-1)$ to get the point $(-1,3)$.

Step4: Draw the line

Draw a straight line passing through the points we have plotted (e.g., $(0,-1)$ and $(1,-5)$ or $(0,-1)$ and $(-1,3)$).

Answer:

To graph the line $y = - 4x-1$:

1. Plot the point $(0,-1)$ (the $y$-intercept).
2. From $(0,-1)$, use the slope $-4$ (move down 4 units and right 1 unit to get $(1,-5)$ or up 4 units and left 1 unit to get $(-1,3)$).
3. Draw a straight line through these points.