Question

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

Explanation:

Step1: Plot the y - intercept

The y - intercept is given as \(y=- 2\). So, we first mark the point \((0,-2)\) on the coordinate plane. This is because the y - intercept is the point where the line crosses the y - axis, and at the y - axis, \(x = 0\).

Step2: Use the slope to find another point

The slope \(m=-\frac{2}{3}\). The slope is defined as \(m=\frac{\text{rise}}{\text{run}}\). A slope of \(-\frac{2}{3}\) means that for a run (change in \(x\)) of \(3\) units (we can choose a positive run to the right), the rise (change in \(y\)) is \(- 2\) units (which means we go down 2 units). Starting from the point \((0,-2)\), if we move \(3\) units to the right (so \(x\) becomes \(0 + 3=3\)) and \(2\) units down (so \(y\) becomes \(-2-2 = - 4\)), we get the point \((3,-4)\). We can also use a run of \(- 3\) (move 3 units to the left) and a rise of \(2\) (move 2 units up). Starting from \((0,-2)\), moving 3 units left (\(x=0 - 3=-3\)) and 2 units up (\(y=-2 + 2=0\)) gives the point \((-3,0)\).

Step3: Draw the line

After plotting the y - intercept \((0,-2)\) and another point (either \((3,-4)\) or \((-3,0)\) or any other point obtained using the slope), we draw a straight line passing through these points.

(Note: Since the problem is about graphing, the final answer is the graph with the line passing through \((0,-2)\) and having a slope of \(-\frac{2}{3}\). If we were to describe the steps in terms of the graphing process, the key points are plotting \((0,-2)\) and then using the slope to find additional points to draw the line.)

Answer:

Step1: Plot the y - intercept

The y - intercept is given as \(y=- 2\). So, we first mark the point \((0,-2)\) on the coordinate plane. This is because the y - intercept is the point where the line crosses the y - axis, and at the y - axis, \(x = 0\).

Step2: Use the slope to find another point

The slope \(m=-\frac{2}{3}\). The slope is defined as \(m=\frac{\text{rise}}{\text{run}}\). A slope of \(-\frac{2}{3}\) means that for a run (change in \(x\)) of \(3\) units (we can choose a positive run to the right), the rise (change in \(y\)) is \(- 2\) units (which means we go down 2 units). Starting from the point \((0,-2)\), if we move \(3\) units to the right (so \(x\) becomes \(0 + 3=3\)) and \(2\) units down (so \(y\) becomes \(-2-2 = - 4\)), we get the point \((3,-4)\). We can also use a run of \(- 3\) (move 3 units to the left) and a rise of \(2\) (move 2 units up). Starting from \((0,-2)\), moving 3 units left (\(x=0 - 3=-3\)) and 2 units up (\(y=-2 + 2=0\)) gives the point \((-3,0)\).

Step3: Draw the line

After plotting the y - intercept \((0,-2)\) and another point (either \((3,-4)\) or \((-3,0)\) or any other point obtained using the slope), we draw a straight line passing through these points.

(Note: Since the problem is about graphing, the final answer is the graph with the line passing through \((0,-2)\) and having a slope of \(-\frac{2}{3}\). If we were to describe the steps in terms of the graphing process, the key points are plotting \((0,-2)\) and then using the slope to find additional points to draw the line.)