Question

graph the line.
y = -2x

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = -2x \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-2 \) and \( b = 0 \). So the line passes through the origin \((0,0)\).

Step2: Find another point

We can use the slope to find another point. The slope \( m=-2=\frac{\text{rise}}{\text{run}}=\frac{- 2}{1}\). Starting from the origin \((0,0)\), if we move 1 unit to the right (run = 1) and 2 units down (rise=-2), we get the point \((1,-2)\). We can also use \( x = 2 \), then \( y=-2\times2=-4 \), so the point \((2, - 4)\) is also on the line.

Step3: Graph the line

Plot the points \((0,0)\), \((1,-2)\), \((2,-4)\) (or other points found using the slope) on the coordinate plane and draw a straight line through them.

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y = - 2x \) passing through the origin with a slope of - 2. But in terms of the process, the steps above help in constructing the graph.)

Answer:

The line \( y=-2x \) is graphed by plotting the origin \((0,0)\) and other points (e.g., \((1, - 2)\), \((2,-4)\), \((-1,2)\) etc.) and drawing a straight line through them. The line has a slope of - 2 and passes through the origin.