In order to graph the equation [tex]\( y = -3x - 2 \)[/tex] and determine which answer matches your graph, follow these steps:
1. Identify the Slope and Y-Intercept:
The equation [tex]\( y = -3x - 2 \)[/tex] is in slope-intercept form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] (the slope) is [tex]\(-3\)[/tex].
- [tex]\( b \)[/tex] (the y-intercept) is [tex]\(-2\)[/tex].
2. Plot the Y-Intercept:
Start by plotting the y-intercept on the graph. This is the point where the line crosses the y-axis.
- The y-intercept is [tex]\(-2\)[/tex], so plot the point [tex]\((0, -2)\)[/tex] on the y-axis.
3. Use the Slope to Find Another Point:
The slope [tex]\(-3\)[/tex] means that for every step you move to the right (positive [tex]\(x\)[/tex]-direction), you move 3 steps down (negative [tex]\(y\)[/tex]-direction), because the slope is negative.
- Starting from the y-intercept [tex]\((0, -2)\)[/tex], move 1 unit to the right (to [tex]\(x = 1\)[/tex]) and 3 units down. This gives the point [tex]\((1, -5)\)[/tex].
- Alternatively, you can move 1 unit to the left (to [tex]\(x = -1\)[/tex]) and 3 units up (since moving left and up still adheres to the slope of [tex]\(-3\)[/tex]). This would give the point [tex]\((-1, 1)\)[/tex].
4. Draw the Line:
Draw a straight line through the points [tex]\((0, -2)\)[/tex] and [tex]\((1, -5)\)[/tex]. Extend the line across the graph to cover all relevant points.
5. Determine the Matching Graph:
Compare the graph you drew with the given options to find the one that matches.
By following these steps, your graph should clearly show a line with a y-intercept at [tex]\((0, -2)\)[/tex] and a slope that descends steeply at a rate of [tex]\(-3\)[/tex]. Use these properties to match it with the correct provided graph.
