Question

graph the line.
y = -3x - 2

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = -3x - 2 \) is in slope - intercept form \( y=mx + b \), where \( m=-3 \) (slope) and \( b = - 2 \) (y - intercept). The y - intercept is the point where the line crosses the y - axis, so when \( x = 0 \), \( y=-2 \). So we have the point \( (0,-2) \).

Step2: Use the slope to find another point

The slope \( m=\frac{\text{rise}}{\text{run}}=-3=\frac{-3}{1} \). From the point \( (0,-2) \), we can go down 3 units (because the rise is - 3) and then 1 unit to the right (because the run is 1). So starting from \( (0,-2) \), \( x=0 + 1=1 \) and \( y=-2-3=-5 \). So we get the point \( (1,-5) \). We can also go up 3 units and left 1 unit from \( (0,-2) \): \( x = 0-1=-1 \), \( y=-2 + 3 = 1 \), so the point \( (-1,1) \) is also on the line.

Step3: Plot the points and draw the line

Plot the points \( (0,-2) \), \( (1,-5) \), \( (-1,1) \) on the coordinate plane and then draw a straight line passing through these points.

(Note: Since this is a graphing problem, the final answer is the graph of the line \( y=-3x - 2 \) passing through points like \( (0,-2) \), \( (1,-5) \), \( (-1,1) \) etc. But in terms of the process, we have identified the key points and the slope to graph the line.)

Answer:

The line \( y = - 3x-2 \) is graphed by plotting the y - intercept \( (0,-2) \) and using the slope \( - 3 \) to find other points (e.g., \( (1,-5) \), \( (-1,1) \)) and then drawing a straight line through them.