Question

Graph the equation y = -2/5x - 3 Click Here for Help Video

Answer 1

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):
1. Move 5 units to the right to (5, -3).
2. 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 \( y = -\frac{2}{5}x - 3 \).