Question

use the slope - intercept form to graph the equation $y = -2x - 1$
use the graphing tool to graph the line. use the slope and y - intercept when
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graph

Explanation:

Step1: Recall Slope-Intercept Form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. For the equation \( y = -2x - 1 \), we identify \( m = -2 \) and \( b = -1 \).

Step2: Plot the Y-Intercept

The y-intercept \( b = -1 \) means the line crosses the y-axis at the point \( (0, -1) \). So we plot the point \( (0, -1) \) on the coordinate plane.

Step3: Use the Slope to Find Another Point

The slope \( m = -2 \) can be written as \( \frac{-2}{1} \) (rise over run). From the y-intercept \( (0, -1) \), we move down 2 units (because the rise is -2) and then 1 unit to the right (because the run is 1). This gives us the point \( (0 + 1, -1 - 2) = (1, -3) \). We can also move up 2 units and left 1 unit from \( (0, -1) \) to get another point, \( (0 - 1, -1 + 2) = (-1, 1) \).

Step4: Draw the Line

Connect the plotted points (e.g., \( (0, -1) \), \( (1, -3) \), \( (-1, 1) \)) with a straight line to graph the equation \( y = -2x - 1 \).

Answer:

To graph \( y = -2x - 1 \):

1. Plot the y-intercept \( (0, -1) \).
2. Use the slope \( -2 \) (rise -2, run 1) to find another point (e.g., \( (1, -3) \) or \( (-1, 1) \)).
3. Draw a straight line through the plotted points.