Question

graph the following features: • y - intercept = 2 • slope = - 3

Explanation:

Step1: Recall the 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 $m=-3$ and $b = 2$, the equation of the line is $y=-3x + 2$.

Step2: Find the y - intercept point

The y - intercept is $b = 2$. So the line crosses the y - axis at the point $(0,2)$. Plot this point on the graph.

Step3: Use the slope to find another point

The slope $m=-3=\frac{\Delta y}{\Delta x}$. Starting from the point $(0,2)$, if we move 1 unit to the right ($\Delta x = 1$), then $\Delta y=-3$. So we move 3 units down. The new point is $(1,-1)$.

Step4: Draw the line

Draw a straight line passing through the points $(0,2)$ and $(1,-1)$.

Answer:

The line with equation $y=-3x + 2$ is graphed by plotting the y - intercept $(0,2)$ and using the slope to find another point $(1,-1)$ and then drawing a line through them.