Question

graph the line.
y = -x

Explanation:

Step1: Identify the slope and intercept

The equation \( y = -x \) is in slope - intercept form \( y=mx + b \), where \( m=- 1 \) (slope) and \( b = 0 \) (y - intercept). So the line passes through the origin \((0,0)\).

Step2: Find another point

Using the slope \( m=-1=\frac{\text{rise}}{\text{run}}=\frac{- 1}{1}\). From the origin \((0,0)\), if we move 1 unit to the right (run = 1) and 1 unit down (rise=-1), we get the point \((1, - 1)\). Similarly, if we move 1 unit to the left (run=-1) and 1 unit up (rise = 1), we get the point \((-1,1)\).

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((1,-1)\), \((-1,1)\) on the coordinate plane and then draw a straight line passing through these points. The line should have a negative slope (going down from left to right) and pass through the origin.

Answer:

To graph \( y=-x \), plot the origin \((0,0)\), then use the slope \(-1\) to find other points (e.g., \((1, - 1)\), \((-1,1)\)) and draw a straight line through them. The line has a slope of \(-1\) and a y - intercept of \(0\).