graph the following features: • slope = -3 • y-intercept = -5

Explanation:

Step1: Recall 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 $b = - 5$, the equation of the line is $y=-3x - 5$.

Step2: Plot the Y - Intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-5$. So we plot the point $(0,-5)$ on the coordinate plane.

Step3: Use the Slope to Find Another Point

The slope $m=-3$ can be written as $\frac{\text{rise}}{\text{run}}=\frac{- 3}{1}$. From the point $(0,-5)$, 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 $(0 + 1,-5-3)=(1,-8)$. We can also move up 3 units and left 1 unit from $(0,-5)$ to get another point $(-1,-2)$ (since $\frac{3}{-1}=-3$).

Step4: Draw the Line

After plotting at least two points (e.g., $(0,-5)$ and $(1,-8)$ or $(0,-5)$ and $(-1,-2)$), we draw a straight line passing through these points to represent the linear equation $y=-3x - 5$.

Answer:

The line is graphed by first plotting the y - intercept at $(0, - 5)$ 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 the plotted points. The equation of the line is $y=-3x - 5$.