Question

graph the line.
$y = -4x + 8$

Explanation:

Step1: Identify the y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-4x + 8\), when \(x = 0\), \(y=8\). So the y - intercept is the point \((0,8)\). We plot this point on the y - axis.

Step2: Use the slope to find another point

The slope \(m=-4=\frac{-4}{1}\). The slope is the ratio of the change in \(y\) to the change in \(x\) (\(m=\frac{\Delta y}{\Delta x}\)). Starting from the y - intercept \((0,8)\), we move down 4 units (because \(\Delta y=- 4\)) and then 1 unit to the right (because \(\Delta x = 1\)). So we get the point \((0 + 1,8-4)=(1,4)\). We can also move up 4 units and left 1 unit from the y - intercept: \((0-1,8 + 4)=(-1,12)\), but \((1,4)\) is easier to plot on the given grid.

Step3: Draw the line

After plotting the points \((0,8)\) and \((1,4)\) (and we can find more points using the slope if needed, like \((2,0)\) since from \((1,4)\), moving down 4 and right 1 gives \((2,0)\)), we draw a straight line passing through these points.

(Note: Since the problem is about graphing, the main steps are identifying the y - intercept, using the slope to find other points, and then drawing the line. If we were to describe the graph, the line has a slope of - 4 and a y - intercept at (0,8), passing through points like (0,8), (1,4), (2,0) etc.)

Answer:

To graph the line \(y=-4x + 8\):

1. Plot the y - intercept \((0,8)\) on the y - axis.
2. Use the slope \(m = - 4\) (rise/run=\(-4/1\)) to find another point. From \((0,8)\), move down 4 units and right 1 unit to get \((1,4)\), or down 4 and right 1 repeatedly to get more points (e.g., \((2,0)\)).
3. Draw a straight line through the plotted points.