Question

graph the following features: - y-intercept = 2 - slope = $-\frac{6}{5}$

Explanation:

Step1: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Given that the y - intercept is 2, we plot the point \((0,2)\) on the coordinate plane.

Step2: Use the slope to find another point

The slope of a line is given by \(m=\frac{\text{rise}}{\text{run}}\). Here, the slope \(m =-\frac{6}{5}\), which means the rise is - 6 (we go down 6 units) and the run is 5 (we go to the right 5 units) or the rise is 6 (we go up 6 units) and the run is - 5 (we go to the left 5 units).
Starting from the point \((0,2)\), if we use the rise of - 6 and run of 5:

• The new \(x\) - coordinate is \(0 + 5=5\)
• The new \(y\) - coordinate is \(2-6=-4\)

So we get the point \((5, - 4)\).
If we use the rise of 6 and run of - 5:

• The new \(x\) - coordinate is \(0-5 = - 5\)
• The new \(y\) - coordinate is \(2 + 6=8\)

So we get the point \((-5,8)\)

Step3: Draw the line

After plotting the points (either \((0,2)\) and \((5,-4)\) or \((0,2)\) and \((-5,8)\)), we draw a straight line passing through these points.

(Note: Since the question is about graphing, the final answer is the graph with the line passing through the points found above. But in text - based form, we can describe the steps to graph it as above.)

Answer:

1. Plot the point \((0,2)\) (the y - intercept).
2. From \((0,2)\), move down 6 units and right 5 units to plot \((5,-4)\) (or move up 6 units and left 5 units to plot \((-5,8)\)).
3. Draw a straight line through the plotted points.