To graph the line represented by the equation \(\( y = -5x + 2 \)\), follow these steps:
1. Understand the Equation Format:
The given equation is in the slope-intercept form \(\( y = mx + b \)\), where:
- \(\( m \)\) is the slope of the line.
- \(\( b \)\) is the y-intercept (the point where the line crosses the y-axis).
Here, \(\( m = -5 \)\) and \(\( b = 2 \)\).
2. Plot the Y-Intercept:
Identify and plot the y-intercept on the graph. The y-intercept is where \(\( x = 0 \)\).
- For \(\( x = 0 \)\), \(\( y = 2 \)\). This gives us the point (0, 2).
3. Use the Slope to Find Another Point:
The slope \(\( m = -5 \)\) can be interpreted as "rise over run":
- In this case, \(\( -5 = \frac{\text{rise}}{\text{run}} \)\), which means for every 1 unit you move to the right (positive \(\( x \)\)-direction), the line goes down by 5 units (negative \(\( y \)\)-direction).
Starting from the y-intercept (0, 2):
- Move 1 unit to the right: \(\( x = 1 \)\).
- Move 5 units down: \(\( y = 2 - 5 = -3 \)\).
This gives another point on the line: (1, -3).
4. Draw the Line:
- Plot the points (0, 2) and (1, -3) on the graph.
- Draw a straight line passing through these points. This line represents the equation \(\( y = -5x + 2 \)\).
Graph Details:
- Use a coordinate plane where the x-values range approximately from -10 to 10 and the y-values similarly.
- Add labels to your axes and a title for clarity.
In summary:
- Plot the y-intercept (0, 2).
- Use the slope to find another point (e.g., (1, -3)).
- Draw a line through these points.
This way, you will have successfully graphed the line represented by the equation \(\( y = -5x + 2 \)\).
