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 \(= 2\), 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 for a run (change in \(x\)) of \(5\) units, the rise (change in \(y\)) is \(- 6\) units (or for a run of \(- 5\) units, the rise is \(6\) units). Starting from the point \((0,2)\), if we move \(5\) units to the right (increase \(x\) by \(5\)) and \(6\) units down (decrease \(y\) by \(6\)), we get the point \((0 + 5,2-6)=(5,-4)\). Alternatively, we can move \(5\) units to the left (decrease \(x\) by \(5\)) and \(6\) units up (increase \(y\) by \(6\)) to get the point \((0 - 5,2 + 6)=(-5,8)\).

Step3: Draw the line

Draw a straight line passing through the points \((0,2)\) and either \((5,-4)\) or \((-5,8)\) (or any other points obtained using the slope from the y - intercept).

Answer:

To graph the line:

1. Plot the point \((0,2)\) (the y - intercept).
2. Use the slope \(m =-\frac{6}{5}\) to find another point (e.g., from \((0,2)\), move 5 units right and 6 units down to get \((5, - 4)\) or 5 units left and 6 units up to get \((-5,8)\)).
3. Draw a straight line through the plotted points.