Question

graph this line using the slope and y-intercept: y = -2x + 2 click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-2x + 2\), \(b = 2\). So the y - intercept is the point \((0,2)\). We plot this point on the graph (where \(x = 0\) and \(y=2\)).

Step2: Determine the slope

The slope \(m=-2\), which can be written as \(\frac{-2}{1}\) (rise over run). From the y - intercept \((0,2)\), we move down 2 units (because the rise is - 2) and then 1 unit to the right (run is 1). This gives us the point \((0 + 1,2-2)=(1,0)\). We can also move up 2 units and left 1 unit from \((0,2)\) to get \((0 - 1,2 + 2)=(-1,4)\) to find another point on the line.

Step3: Draw the line

After plotting at least two points (e.g., \((0,2)\) and \((1,0)\) or \((0,2)\) and \((-1,4)\)), we draw a straight line passing through these points.

Answer:

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

1. Plot the y - intercept \((0,2)\) (since when \(x = 0\), \(y=2\)).
2. Use the slope \(m=-2=\frac{-2}{1}\): from \((0,2)\), move down 2 units and right 1 unit to get \((1,0)\), or up 2 units and left 1 unit to get \((-1,4)\).
3. Draw a straight line through the plotted points. The line should pass through \((0,2)\), \((1,0)\), \((-1,4)\) etc.