Question

graph the following features: - slope = 1/3 - y-intercept = -1

Explanation:

Answer:

To graph the line with slope \(\frac{1}{3}\) and y - intercept \(- 1\):

Step 1: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. For a y - intercept of \(-1\), we plot the point \((0,-1)\) on the coordinate plane.

Step 2: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}=\frac{1}{3}\). This means that from the point \((0, - 1)\), we move up \(1\) unit (rise) and then move to the right \(3\) units (run).
Starting from \((0,-1)\), moving up \(1\) unit gives us a y - coordinate of \(-1 + 1=0\), and moving right \(3\) units gives us an x - coordinate of \(0+3 = 3\). So we get the point \((3,0)\).

Step 3: Draw the line

Draw a straight line passing through the points \((0,-1)\) and \((3,0)\). We can also find more points using the slope (for example, from \((3,0)\), moving up \(1\) and right \(3\) gives \((6,1)\)) to make the line more accurate, but two points are enough to define a straight line.

The equation of the line in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) is \(y=\frac{1}{3}x-1\), and the graph is a straight line passing through \((0, - 1)\) with a positive slope of \(\frac{1}{3}\).