To graph the equation [tex]\( y = -\frac{2}{3}x + 5 \)[/tex], follow these steps:
### Step 1: Plot the y-intercept
- The y-intercept is the point where the line crosses the y-axis. This point occurs when [tex]\( x = 0 \)[/tex].
- From the equation [tex]\( y = -\frac{2}{3}x + 5 \)[/tex], we can see that when [tex]\( x = 0 \)[/tex], [tex]\( y = 5 \)[/tex]. Therefore, the y-intercept is [tex]\( (0, 5) \)[/tex].
- Plot the point [tex]\( (0, 5) \)[/tex] on the graph.
### Step 2: Use the slope to find another point
- The slope of the line is [tex]\( -\frac{2}{3} \)[/tex]. This means that for every 3 units you move to the right, you move 2 units down.
- Starting from the y-intercept [tex]\( (0, 5) \)[/tex], move 3 units to the right, which takes you to [tex]\( x = 3 \)[/tex]. From there, move 2 units down, which takes you from [tex]\( y = 5 \)[/tex] to [tex]\( y = 3 \)[/tex].
- Therefore, another point on the line is [tex]\( (3, 3) \)[/tex].
- Plot the point [tex]\( (3, 3) \)[/tex] on the graph.
### Step 3: Connect the points
- Draw a straight line through the points [tex]\( (0, 5) \)[/tex] and [tex]\( (3, 3) \)[/tex] using a straightedge. This line represents the equation [tex]\( y = -\frac{2}{3}x + 5 \)[/tex].
By following these steps, you should have accurately graphed the equation.
