Question

graph the line.
$y = -2x - 2$

Explanation:

Step1: Identify the slope and y-intercept

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

Step2: Plot the y-intercept

The y - intercept is \( b=-2 \), so we plot the point \( (0,-2) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m=-2=\frac{-2}{1} \). From the point \( (0,-2) \), we move down 2 units (because the numerator of the slope is - 2) and then 1 unit to the right (because the denominator of the slope is 1). This gives us the point \( (1,-4) \). We can also move up 2 units and 1 unit to the left (since \( \frac{-2}{1}=\frac{2}{-1} \)) from \( (0,-2) \) to get the point \( (-1,0) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \( (0,-2) \) and \( (1,-4) \) or \( (0,-2) \) and \( (-1,0) \)).

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y = - 2x-2 \) with the y - intercept at \( (0,-2) \) and passing through other points determined by the slope. If we were to describe the key points: the y - intercept is \( (0, - 2) \) and another point can be \( (1,-4) \) or \( (-1,0) \) and the line connects these points with a slope of - 2.)

Answer:

The line \( y=-2x - 2 \) has a y - intercept at \( (0,-2) \) and a slope of - 2. To graph it, plot \( (0,-2) \), then use the slope to find another point (e.g., \( (1,-4) \) or \( (-1,0) \)) and draw a straight line through these points.