Question

graph the line with the equation $y = -x + 2$.

Explanation:

Step1: Identify the y-intercept

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

Step2: Determine the slope

The slope \(m\) of the line \(y=-x + 2\) is \(- 1\) (since \(y=-1x + 2\)). The slope \(m=\frac{\text{rise}}{\text{run}}=-1=\frac{-1}{1}\) or \(\frac{1}{-1}\).

Step3: Find another point

Using the y - intercept \((0,2)\) and the slope. If we use the slope \(\frac{-1}{1}\), from \((0,2)\), we move down 1 unit and right 1 unit to get the point \((1,1)\). If we use the slope \(\frac{1}{-1}\), from \((0,2)\), we move up 1 unit and left 1 unit to get the point \((-1,3)\).

Step4: Draw the line

Plot the points \((0,2)\), \((1,1)\) (or \((-1,3)\)) and draw a straight line through them.

(Note: Since the problem is about graphing, the final answer is the graph of the line \(y=-x + 2\) passing through \((0,2)\) and other points determined by the slope, like \((1,1)\) or \((-1,3)\) etc.)

Answer:

The line \(y = -x+2\) is graphed by plotting the y - intercept \((0,2)\) and using the slope \(-1\) to find another point (e.g., \((1,1)\) or \((-1,3)\)) and then drawing a straight line through these points.