To graph the line that represents the equation [tex]\( y = -\frac{2}{3}x + 1 \)[/tex], follow these steps:
1. Identify the y-intercept: This is the point where the line crosses the y-axis. The equation [tex]\( y = -\frac{2}{3}x + 1 \)[/tex] is in slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- In this case, the y-intercept ([tex]\( b \)[/tex]) is 1.
- Plot the point (0, 1) on the graph.
2. Determine the slope: The slope [tex]\( m \)[/tex] is [tex]\(-\frac{2}{3}\)[/tex].
- This means that for every 3 units you move to the right (positive direction on the x-axis), you will move 2 units down (negative direction on the y-axis).
3. Plot a second point using the slope:
- From the y-intercept (0, 1), move 3 units to the right to (3, 1).
- From (3, 1), move 2 units down to (3, -1).
- Plot the point (3, -1).
4. Draw the line: Draw a straight line through the points (0, 1) and (3, -1). This is the graph of the equation [tex]\( y = -\frac{2}{3}x + 1 \)[/tex].
By following these steps, you will have the correct graph of the line [tex]\( y = -\frac{2}{3}x + 1 \)[/tex] on your coordinate plane.
