Question

graph the line.
y = -4x + 8

Explanation:

Step1: Identify the y-intercept

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

Step2: Determine the slope

The slope \(m=-4=\frac{-4}{1}\). The slope is the rise over run. From the y - intercept \((0,8)\), we can go down 4 units (because the numerator of the slope is - 4, which means a decrease) and then 1 unit to the right (because the denominator of the slope is 1, which means a move in the positive x - direction). This gives us the point \((0 + 1,8-4)=(1,4)\). We can also go up 4 units and left 1 unit (using the slope \(\frac{4}{-1}\)) from the y - intercept to get another point, for example, \((-1,12)\).

Step3: Draw the line

After plotting two or more points (like \((0,8)\) and \((1,4)\) or \((-1,12)\)), draw a straight line passing through these points.

Answer:

The line \(y = - 4x+8\) is graphed by first plotting the y - intercept \((0,8)\) and then using the slope \(-4\) to find additional points and drawing a straight line through them.