To graph the line that represents the equation [tex]\( y = -\frac{2}{3} x + 1 \)[/tex], follow these steps:
1. Identify the y-intercept:
The equation [tex]\( y = -\frac{2}{3} x + 1 \)[/tex] 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.
- In this equation, the y-intercept ([tex]\( b \)[/tex]) is 1. This means the line crosses the y-axis at the point (0, 1).
2. Plot the y-intercept:
- Start by plotting the point (0, 1) on the graph.
3. 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 along the x-axis, the value of y decreases by 2 units.
4. Use the slope to find another point:
- From the y-intercept (0, 1), move 3 units to the right along the x-axis to reach [tex]\( x = 3 \)[/tex].
- Then, move 2 units down along the y-axis to [tex]\( y = -1 \)[/tex]. This gives you the point (3, -1).
5. Plot the second point:
- Plot the point (3, -1) on the graph.
6. Draw the line:
- Use a ruler to draw a straight line through the points (0, 1) and (3, -1).
Here is a summary of our findings and actions:
- Y-intercept: Plot the point (0, 1).
- Second point using the slope: Plot the point (3, -1).
- Draw a straight line through these two points to form the graph of the equation [tex]\( y = -\frac{2}{3} x + 1 \)[/tex].
Upon graphing, you should see a downward-sloping straight line that crosses the y-axis at (0, 1) and passes through the point (3, -1).
