Scott and Brooke are organizing a fundraiser for their school. They are planning a pasta dinner, where adult tickets will cost $16 and kids' tickets will cost $8. Their goal is to make $2000. If they sell only adult tickets, how many must they sell to reach their goal? If they sell only kids' tickets, how many must they sell to reach their goal?
Graphing a Line in Standard Form
When a line is in standard form, there are two different ways to graph it. The first is to change the equation to slope-intercept form and then graph as shown in the previous concept. The second is to use standard form to find the
Graph the following equation
Let’s use approach #1; change the equation to slope-intercept form.
Find the x and y intercepts of the equation
Recall the Standard Form concept. The other coordinate will be zero at these points. Therefore, for the
Graph the equation from previous problem
Use approach #2 from above. Plot each intercept from the previous problem on their respective axes and draw a line to connect them.
Earlier, you were asked how many adult and kids' tickets must they sell to reach their goal.
The equation, in standard form, for the pasta dinner sales goal is
Therefore, they must sell 125 adult tickets to reach their goal.
If they sell only kids' tickets, we are looking for the y-intercept, so set x equal to zero.
Therefore, they must sell 250 kids' tickets to reach their goal.
Substitute in zero for
Now, plot each on their respective axes and draw a line.
Graph the following lines by changing the equation to slope-intercept form.
−2x+y=5 3x+8y=16 4x−2y=10 6x+5y=−20 9x−6y=24 x+4y=−12
Graph the following lines by finding the intercepts.
2x+3y=12 −4x+5y=30 x−2y=8 7x+y=−7 6x+10y=15 4x−8y=−28 y=3
- Writing Which method do you think is easier? Why?
- Writing Which method would you use to graph
Answers for Review Problems
To see the Review answers, open this PDF file and look for section 2.7.