Question

graph this line using the slope and y-intercept:
y = -4x + 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 labeled)

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-4x + 2\), \(b = 2\). So the line crosses the y - axis at \((0,2)\).

Step2: Determine the slope

The slope \(m=-4=\frac{-4}{1}\). The slope is the rise over run. From the y - intercept \((0,2)\), we can go down 4 units (because the slope is negative) and then 1 unit to the right. So from \((0,2)\), moving down 4 gives \(y = 2-4=-2\) and moving right 1 gives \(x = 0 + 1=1\). So another point on the line is \((1,-2)\). We can also go up 4 units and left 1 unit from \((0,2)\): \(y=2 + 4 = 6\) and \(x=0-1=-1\), so the point \((-1,6)\) is also on the line. To graph the line, we plot the points \((0,2)\), \((1,-2)\), \((-1,6)\) (or other points found using the slope) and draw a straight line through them.

Answer:

To graph \(y=-4x + 2\):

1. Plot the y - intercept at \((0,2)\) (since when \(x = 0\), \(y=2\)).
2. Use the slope \(m=-4=\frac{\text{rise}}{\text{run}}=\frac{-4}{1}\):

• From \((0,2)\), move down 4 units and right 1 unit to get the point \((1,-2)\).
• Or move up 4 units and left 1 unit to get the point \((-1,6)\).

1. Draw a straight line through the plotted points (e.g., \((0,2)\), \((1,-2)\), \((-1,6)\)).