To graph the equation \( y = -\frac{2}{5}x - 3 \), you can follow these steps:
Step 1: Identify the slope and y-intercept
The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope
- \( b \) is the y-intercept
From the equation \( y = -\frac{2}{5}x - 3 \):
- The slope (\( m \)) is \( -\frac{2}{5} \).
- The y-intercept (\( b \)) is \( -3 \).
Step 2: Plot the y-intercept
Start by plotting the y-intercept on the graph. The y-intercept is the point where the line crosses the y-axis:
- The y-intercept is at the point (0, -3).
Step 3: Use the slope to find another point
The slope \( -\frac{2}{5} \) means that for every 5 units you move to the right (positive x-direction), you move down 2 units (negative y-direction).
From the y-intercept (0, -3):
- Move 5 units to the right to (5, -3).
- Move 2 units down to (5, -5).
Now you have another point at (5, -5).
Step 4: Plot the second point
Plot the point (5, -5) on the graph.
Step 5: Draw the line
Now draw a straight line through the points (0, -3) and (5, -5). This line represents the equation \( y = -\frac{2}{5}x - 3 \).
Optional Step: Additional Points
To ensure accuracy, you might want to find and plot additional points:
- For \( x = -5 \): \[ y = -\frac{2}{5}(-5) - 3 = 2 - 3 = -1 \] So, the point (-5, -1) can be plotted as well.
Summary
To summarize, the key points to plot are:
- (0, -3) - y-intercept
- (5, -5) - calculated using slope
- (-5, -1) - optionally added point
After plotting these points and connecting them with a straight line, you will have successfully graphed the equation \( y = -\frac{2}{5}x - 3 \).