Final answer:
To graph the equation -14x+21y=84, we solve for y to obtain the slope-intercept form y = (2/3)x + 4, create a table of values, plot the points, and draw a line through the points on a graph.
Step-by-step explanation:
To graph the equation -14x+21y=84, first, we need to convert it to slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We can do this by isolating y on one side of the equation:
- Add 14x to both sides: 21y = 14x + 84.
- Divide everything by 21 to solve for y: y = (14/21)x + (84/21).
- Simplify: y = (2/3)x + 4.
Now that we have y = (2/3)x + 4, we can create a table of values by plugging in different values for x and then calculate the corresponding y values. For example, if x is 0, then y is 4. If x is 3, then y is 6. Once we have a table of values, we plot these points on a graph and draw a line through them, representing the equation.