To draw the line representing the equation [tex]\( y = -\frac{2}{3} x + 1 \)[/tex] on a graph, follow these steps:
1. Identify the y-intercept:
The equation of the line is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Here, the y-intercept [tex]\( b \)[/tex] is 1. This means the line crosses the y-axis at [tex]\( (0, 1) \)[/tex].
- Plot the point (0, 1) on the graph.
2. Determine another point using the slope:
The slope [tex]\( m \)[/tex] is [tex]\(-\frac{2}{3} \)[/tex], which means for every 3 units you move to the right on the x-axis, you move 2 units down on the y-axis.
Starting from the y-intercept (0, 1):
- Move 3 units to the right. This lands you at [tex]\( x = 3 \)[/tex].
- Move 2 units down. Since our starting y-coordinate was 1, moving 2 units down lands us at [tex]\( y = -1 \)[/tex].
- Plot the point (3, -1).
3. Draw the line:
Using a ruler or the line drawing tool available, draw a straight line through the points (0, 1) and (3, -1).
4. Extend the line:
Extend the line through both directions to cover the entire graph, ensuring it accurately represents the equation [tex]\( y = -\frac{2}{3} x + 1 \)[/tex].
Here's a quick reference to help visualize the points and line:
- Initial point at y-intercept (0, 1)
- Slope calculation to find second point (3, -1)
- Draw a straight line through these points and extend it across the graph.
By following these steps, you’ll correctly draw the line for the equation [tex]\( y = -\frac{2}{3} x + 1 \)[/tex].
