Question

graph this line using the slope and y-intercept:
y = -3x - 1
click to select points on the graph.

Explanation:

Step1: Identify slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-3x - 1\), the slope \(m=-3\) (or \(\frac{-3}{1}\)) and the y - intercept \(b = - 1\). So, the line crosses the y - axis at the point \((0,-1)\).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,-1)\) (since when \(x = 0\), \(y=-1\)) and mark it.

Step3: Use the slope to find another point

The slope \(m=\frac{-3}{1}\) means for every 1 unit we move to the right (increase in \(x\) by 1), we move down 3 units (decrease in \(y\) by 3). Starting from \((0,-1)\), if we move 1 unit to the right (to \(x = 1\)) and 3 units down, we get the point \((1,-1 - 3)=(1,-4)\). We can also move in the opposite direction: for a slope of \(\frac{-3}{1}\), we can think of it as \(\frac{3}{-1}\), so moving 1 unit to the left (decrease \(x\) by 1) and 3 units up (increase \(y\) by 3) from \((0,-1)\) gives \((-1,-1 + 3)=(-1,2)\).

Step4: Draw the line

Connect the points (e.g., \((0,-1)\), \((1,-4)\), \((-1,2)\)) with a straight line to graph the equation \(y=-3x - 1\).

Answer:

To graph \(y = - 3x-1\): 1. Plot the y - intercept \((0,-1)\). 2. Use the slope \(-3\) (rise - 3, run 1 or rise 3, run - 1) to find another point (e.g., \((1,-4)\) or \((-1,2)\)). 3. Draw a straight line through the plotted points.