Question

graph the following features: - slope = $-\frac{3}{2}$ - y-intercept = 5

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 $b = 5$, the equation of the line is $y=-\frac{3}{2}x + 5$.

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 $m =-\frac{3}{2}$ can be thought of as $\frac{\text{rise}}{\text{run}}=\frac{- 3}{2}$. Starting from the point $(0,5)$, we move down 3 units (because the rise is - 3) and then move 2 units to the right (because the run is 2). This gives us the point $(0 + 2,5-3)=(2,2)$. We can also move up 3 units and left 2 units from $(0,5)$ to get the point $(0 - 2,5 + 3)=(-2,8)$.

Step4: Draw the line

After plotting the points (e.g., $(0,5)$, $(2,2)$, $(-2,8)$), we draw a straight line passing through these points to represent the linear equation.

Answer:

To graph the line with slope $-\frac{3}{2}$ and y - intercept 5:

1. Plot the y - intercept at $(0,5)$.
2. Use the slope $-\frac{3}{2}$ (down 3, right 2 or up 3, left 2 from the y - intercept) to find additional points (e.g., $(2,2)$ or $(-2,8)$).
3. Draw a straight line through the plotted points.