Question

graph this line using the slope and y-intercept:
$y = -8x - 1$
click to select points on the graph.

Explanation:

Step1: Identify the slope and y-intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-8x - 1\), the slope \(m=-8\) (or \(\frac{-8}{1}\)) and the y - intercept \(b=-1\). This means the line crosses the y - axis at the point \((0,-1)\).

Step2: Plot the y - intercept

First, we plot the y - intercept point \((0,-1)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m = \frac{\text{rise}}{\text{run}}=\frac{-8}{1}\). Starting from the y - intercept \((0,-1)\), we move down 8 units (because the rise is - 8) and then 1 unit to the right (because the run is 1). So we move from \((0,-1)\) to \((0 + 1,-1-8)=(1,-9)\). Alternatively, we can move up 8 units (since \(\frac{8}{-1}\) is also equivalent to the slope - 8, moving up 8 and left 1) from \((0,-1)\) to \((0 - 1,-1 + 8)=(-1,7)\).

Step4: Draw the line

After plotting at least two points (e.g., \((0,-1)\) and \((1,-9)\) or \((0,-1)\) and \((-1,7)\)), we draw a straight line passing through these points.

To graph the line \(y=-8x - 1\):

1. Plot the y - intercept: The point \((0,-1)\) (since when \(x = 0\), \(y=-1\)).
2. Use the slope: From \((0,-1)\), since the slope \(m=-8=\frac{-8}{1}\), move 8 units down (in the negative y - direction) and 1 unit to the right (in the positive x - direction) to get the point \((1,-9)\), or 8 units up and 1 unit to the left to get \((-1,7)\).
3. Draw a straight line through the plotted points.

(Note: Since the problem asks to graph the line, the key points to plot are \((0,-1)\) and another point found using the slope, and then draw the line connecting them.)

Answer:

The line is graphed by first plotting the y - intercept \((0,-1)\) and then using the slope \(-8\) to find another point (e.g., \((1,-9)\) or \((-1,7)\)) and drawing a straight line through these points.