Question

graph the following features: - slope = \\(\frac{4}{3}\\) - y-intercept = \\(-4\\)

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 $m=\frac{4}{3}$ and the y - intercept $b = - 4$, the equation of the line is $y=\frac{4}{3}x-4$.

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When $x = 0$, $y=-4$. So we plot the point $(0,-4)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m=\frac{4}{3}$ can be thought of as $\frac{\text{rise}}{\text{run}}=\frac{4}{3}$. This means that from the point $(0, - 4)$, we can move up 4 units (because the numerator of the slope is positive) and then move to the right 3 units (because the denominator of the slope is positive).
Starting from $(0,-4)$:

• Rise: $y=-4 + 4=0$
• Run: $x = 0+3 = 3$

So we get the point $(3,0)$. We can also move down 4 units and left 3 units from $(0,-4)$ to get another point. If we move down 4 units, $y=-4-4=-8$, and left 3 units, $x = 0 - 3=-3$, so we get the point $(-3,-8)$.

Step4: Draw the line

After plotting the points (e.g., $(0,-4)$ and $(3,0)$ or $(0,-4)$ and $(-3,-8)$), we draw a straight line passing through these points.

To graph the line:

1. Plot the point \((0, - 4)\) (the y - intercept).
2. From \((0, - 4)\), move up 4 units and right 3 units to plot the point \((3,0)\) (or down 4 units and left 3 units to plot \((-3,-8)\)).
3. Draw a straight line connecting these points (and extending it in both directions).

(Note: Since the problem asks to graph the features, the key steps are plotting the y - intercept and then using the slope to find another point to draw the line. The final "answer" in terms of the graph is the line represented by \(y=\frac{4}{3}x - 4\) passing through \((0,-4)\) and other points found using the slope.)

Answer:

The line with equation \(y=\frac{4}{3}x - 4\) is graphed by plotting \((0,-4)\) and using the slope \(\frac{4}{3}\) to find additional points (e.g., \((3,0)\)) and drawing a straight line through them.