Final Answer:
In graphing the function 3x + y = 8, the slope should be determined and must be plotted along with a known point. The slope and y-intercept is -3 and 8 respectively.
Step-by-step explanation:
To graph the linear function 3x + y = 8, you can follow these steps:
1. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Start by isolating y on one side of the equation:
```
3x + y = 8
y = -3x + 8
```
Now the equation is in slope-intercept form.
2. Identify the slope (m) and the y-intercept (b):
In the equation y = -3x + 8:
- The slope m is -3: This means that for every unit increase in x, y will decrease by 3 units.
- The y-intercept b is 8: This is the point where the line crosses the y-axis. In other words, when x is 0, y is 8.
3. Plot the y-intercept on the graph:
Locate the point (0, 8) on the y-axis and put a point.
4. Use the slope to find another point:
Starting at the y-intercept (0, 8), use the slope to find another point:
- Since the slope is -3, you can move three units down (because it's negative) and one unit to the right (since we're considering an increase of 1 in x) from the y-intercept to find a new point, (1, 5). Place a point there.
5. Draw the line:
Use a ruler to draw a straight line through both points. This line represents the graph of the function 3x + y = 8.
6. Check your work:
You can check your work by picking another value of x, plugging it into the equation to solve for y, and seeing if that point also lies on your line. For example, if x = 2:
```
y = -3(2) + 8
y = -6 + 8
y = 2
```
So the point (2, 2) should be on the line. If it is not, there may be a mistake in your graph.
By following these steps, you will have successfully graphed the function 3x + y = 8, and your graph will show a straight line with a negative slope, crossing the y-axis at the point (0, 8).