To graph the line represented by the equation [tex]\( y = -5x + 2 \)[/tex], follow these steps:
1. Understand the Equation Format:
The given equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept (the point where the line crosses the y-axis).
Here, [tex]\( m = -5 \)[/tex] and [tex]\( b = 2 \)[/tex].
2. Plot the Y-Intercept:
Identify and plot the y-intercept on the graph. The y-intercept is where [tex]\( x = 0 \)[/tex].
- For [tex]\( x = 0 \)[/tex], [tex]\( y = 2 \)[/tex]. This gives us the point (0, 2).
3. Use the Slope to Find Another Point:
The slope [tex]\( m = -5 \)[/tex] can be interpreted as "rise over run":
- In this case, [tex]\( -5 = \frac{\text{rise}}{\text{run}} \)[/tex], which means for every 1 unit you move to the right (positive [tex]\( x \)[/tex]-direction), the line goes down by 5 units (negative [tex]\( y \)[/tex]-direction).
Starting from the y-intercept (0, 2):
- Move 1 unit to the right: [tex]\( x = 1 \)[/tex].
- Move 5 units down: [tex]\( y = 2 - 5 = -3 \)[/tex].
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 [tex]\( y = -5x + 2 \)[/tex].
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 [tex]\( y = -5x + 2 \)[/tex].
