Question

graph the second linear equation
the equation $y = -x + 2$ has a y-intercept of 2 and a slope of -1. plot the y-intercept at (0, 2). use the slope to find another point. for example, move 1 unit to the right and 1 unit down to the point (1, 1). draw a line through these two points.

Explanation:

Step1: Identify 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 we plot the point \((0,2)\) on the coordinate plane.

Step2: Use slope to find another point

The slope \(m=-1=\frac{-1}{1}\). The slope is the ratio of the change in \(y\) (rise) to the change in \(x\) (run). Starting from \((0,2)\), a run of \(1\) (moving \(1\) unit to the right along the \(x\) - axis) and a rise of \(- 1\) (moving \(1\) unit down along the \(y\) - axis) gives us the point \((0 + 1,2-1)=(1,1)\).

Step3: Draw the line

Using a straight - edge, draw a line that passes through the points \((0,2)\) and \((1,1)\). This line represents the graph of the linear equation \(y=-x + 2\).

Answer:

The graph of \(y =-x + 2\) is a straight line passing through the points \((0,2)\) and \((1,1)\) (and other points found by continuing to use the slope) with a slope of \(-1\) and a y - intercept of \(2\).