Question

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

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 $m=\frac{3}{2}$ and the y - intercept $b = - 2$, the equation of the line is $y=\frac{3}{2}x-2$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-2$. So we plot the point $(0,-2)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m=\frac{3}{2}$ can be thought of as $\frac{\text{rise}}{\text{run}}=\frac{3}{2}$. From the point $(0, - 2)$, we move up 3 units (because the rise is 3) and then move to the right 2 units (because the run is 2). This gives us the point $(0 + 2,-2+3)=(2,1)$.

Step4: Draw the line

Now that we have two points, $(0,-2)$ and $(2,1)$, we can draw a straight line passing through these two points. This line represents the equation $y = \frac{3}{2}x-2$ with the given slope and y - intercept.

Answer:

To graph the line with slope $\frac{3}{2}$ and y - intercept - 2:

1. Plot the point $(0, - 2)$ (the y - intercept).
2. From $(0,-2)$, move up 3 units and right 2 units to plot the point $(2,1)$.
3. Draw a straight line through $(0,-2)$ and $(2,1)$.