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 using the slope

The slope \( m=-2=\frac{-2}{1}\), which means for a run of \( 1 \) (increase in \( x \) by \( 1 \)), the rise is \( - 2 \) (decrease in \( y \) by \( 2 \)). Starting from \((0,0)\), if we move \( x = 1 \), then \( y=-2(1)=-2 \), so we get the point \((1, - 2)\). We can also use a run of \( - 1 \) (decrease in \( x \) by \( 1 \)) and a rise of \( 2 \) (increase in \( y \) by \( 2 \)), so from \((0,0)\), moving \( x=-1\), \( y = - 2\times(-1)=2\), giving the point \((-1,2)\).

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((1,-2)\) (or \((-1,2)\)) on the coordinate plane. Then use a straight - edge to draw a line passing through these points. The line should extend in both directions to represent all the solutions of the equation \( y=-2x \).

(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. If we were to describe the key points, the line passes through \((0,0)\) and \((1, - 2)\) (and other points following the slope), and is a straight line with a negative slope.)

Answer:

The line \( y=-2x \) is graphed by plotting the points \((0,0)\) and \((1, - 2)\) (or other points determined by the slope \( - 2\)) and drawing a straight line through them, extending in both directions.