Question

graph the following features: - slope = -3 - y-intercept = -1

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the slope $m=-3$ and the y - intercept $b = - 1$, the equation of the line is $y=-3x - 1$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-1$. So we plot the point $(0,-1)$ on the graph.

Step3: Use the slope to find another point

The slope $m=\frac{\text{rise}}{\text{run}}=-3=\frac{-3}{1}$. Starting from the point $(0,-1)$, we move down 3 units (because the rise is - 3) and then 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,-1-3)=(1,-4)$. We can also move up 3 units and left 1 unit from $(0,-1)$ to get the point $(-1,2)$ (since $\frac{3}{-1}=-3$ as well).

Step4: Draw the line

Draw a straight line passing through the points we have plotted (e.g., $(0,-1)$ and $(1,-4)$ or $(0,-1)$ and $(-1,2)$). The line should extend in both directions to represent the linear function.

Answer:

The line is graphed by first plotting the y - intercept at $(0, - 1)$ and then using the slope of - 3 (either moving down 3 and right 1 or up 3 and left 1 from the y - intercept) to find another point, and then drawing a straight line through these points. The equation of the line is $y=-3x - 1$.