To graph the function [tex]\( y = -\frac{3}{5}x + 2 \)[/tex], follow these steps:
1. Identify the slope and y-intercept:
- The equation 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.
- For the given function [tex]\( y = -\frac{3}{5}x + 2 \)[/tex], the slope [tex]\( m = -\frac{3}{5} \)[/tex] and the y-intercept [tex]\( b = 2 \)[/tex].
2. Plot the y-intercept:
- Start by plotting the y-intercept on the coordinate plane. Since [tex]\( b = 2 \)[/tex], plot the point (0, 2).
3. Use the slope to find another point:
- The slope [tex]\( -\frac{3}{5} \)[/tex] indicates that for every 5 units you move to the right (positive direction on the x-axis), you move 3 units down (negative direction on the y-axis).
- From the point (0, 2), move 5 units to the right to reach [tex]\( x = 5 \)[/tex]. Then, move 3 units down to reach [tex]\( y = -1 \)[/tex]. Plot the point (5, -1).
4. Draw the line:
- Use a ruler to draw a straight line through the points (0, 2) and (5, -1). This line represents the graph of the function [tex]\( y = -\frac{3}{5}x + 2 \)[/tex].
5. Extend the line in both directions:
- Extend the line through the plotted points across the entire coordinate plane to represent the continuous nature of the linear function.
Your final graph should display a straight line that crosses the y-axis at (0, 2) and passes through the point (5, -1), accurately representing the linear equation [tex]\( y = -\frac{3}{5}x + 2 \)[/tex]. Here are a few calculated points and their corresponding values to help verify the graph:
- At [tex]\( x = -10 \)[/tex], [tex]\( y \approx 8 \)[/tex]
- At [tex]\( x = 0 \)[/tex], [tex]\( y = 2 \)[/tex] (previously identified intercept)
- At [tex]\( x = 5 \)[/tex], [tex]\( y \approx -1 \)[/tex]
- At [tex]\( x = 10 \)[/tex], [tex]\( y \approx -4 \)[/tex]
These points help confirm the correct plotting of the line on the graph.
