Question

graph this line using the slope and y-intercept:
y = -3x - 2
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and axes arrows)

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-3x - 2\), \(b=-2\). So the y - intercept is at the point \((0,-2)\).

Step2: Identify the slope

The slope \(m=-3\), which can be written as \(\frac{-3}{1}\) (rise over run). From the y - intercept \((0,-2)\), we move down 3 units (because the rise is - 3) and 1 unit to the right (run is 1) to get the next point \((0 + 1,-2-3)=(1,-5)\). We can also move up 3 units and 1 unit to the left: \((0 - 1,-2 + 3)=(-1,1)\).

To graph the line, we plot the y - intercept \((0,-2)\) and then use the slope to find other points. For example, starting at \((0,-2)\), using the slope \(\frac{-3}{1}\), we can find more points on the line.

Answer:

To graph \(y = - 3x-2\):

1. Plot the y - intercept at \((0,-2)\) (since when \(x = 0\), \(y=-2\)).
2. Use the slope \(m=-3=\frac{-3}{1}\). From \((0,-2)\), move 1 unit to the right (increase \(x\) by 1) and 3 units down (decrease \(y\) by 3) to get the point \((1,-5)\). Or move 1 unit to the left (decrease \(x\) by 1) and 3 units up (increase \(y\) by 3) to get the point \((-1,1)\).
3. Draw a straight line through the plotted points (e.g., \((0,-2)\), \((1,-5)\), \((-1,1)\) etc.).