Question

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

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 y - intercept $b=-3$ and the slope $m = 3$, the equation of the line is $y=3x - 3$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-3$. So we plot the point $(0,-3)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m = 3=\frac{3}{1}$, which means for a change in $x$ (run) of 1 unit, the change in $y$ (rise) is 3 units. Starting from the point $(0,-3)$, if we move 1 unit to the right (increase $x$ by 1, so $x=0 + 1=1$) and 3 units up (increase $y$ by 3, so $y=-3+3 = 0$), we get the point $(1,0)$. We can also move in the opposite direction: from $(0,-3)$, move 1 unit to the left ( $x = 0-1=-1$) and 3 units down ( $y=-3 - 3=-6$) to get the point $(-1,-6)$.

Step4: Draw the line

Using a straight - edge, draw a line that passes through the points we have plotted (such as $(0,-3)$ and $(1,0)$ or other points found using the slope) to represent the linear equation $y = 3x-3$.

(Note: Since the problem is about graphing, the final answer is the graph of the line with y - intercept - 3 and slope 3. To describe the graphing process, we have followed the steps above. If we were to represent the line, it is a straight line passing through $(0, - 3)$ with a steep positive slope (since slope = 3) and also passing through points like $(1,0)$, $(2,3)$ etc.)

Answer:

The graph is a straight line with a y - intercept at the point $(0,-3)$ and a slope of 3. To construct it, plot $(0,-3)$, then use the slope (rise 3, run 1) to find other points (e.g., $(1,0)$) and draw a line through these points.