At a football game, Brian is selling concessions. He sells soda for $2 apiece and popcorn for $3 per bag. At the end of the night, he has sold out of soda and has made a total of $264. If he sold 60 sodas, how many bags of popcorn did he sell?
Guidance
Slopeintercept form is one way to write the equation of a line. Another way is called standard form. Standard form looks like
Example A
Find the equation of a line, in standard form, where the slope is
Solution: To find the equation in standard form, you need to determine what
In slopeintercept form, the equation is
To change this to standard form we need to subtract the
Example B
The equation of a line is
Solution: To find the slope and
From this, the slope is
Example C
Find the equation of the line below, in standard form.
Solution: Here, we are given the intercepts. The slope triangle is drawn by the axes,
Example D
The equation of a line is
Solution: For the
The
For the
The
Intro Problem Revisit This type of problem is easier to write in standard form. We will call x the number of sodas and y the number of bags of popcorn. The coefficients are the cost of each item in dollars. The expression will equal the total amount of concessions Brian sold.
Now, we know that
Therefore, Brian sold 48 bags of popcorn.
Guided Practice
1. Find the equation of the line, in standard form that passes through (8, 1) and (4, 2).
2. Change
3. What are the intercepts of
Answers
1. Like with Example A, we need to first find the equation of this line in
Find the
The equation of the line is
To change this equation into standard form, add the
2. To change
3. Copy Example D to find the intercepts of
Now, start over and plug in zero for
Explore More
Change the following equations into standard form.

y=−23x+4 
y=x−5 
y=15x−1
Change the following equations into slopeintercept form.

4x+5y=20 
x−2y=9 
2x−3y=15
Find the

3x+4y=12 
6x−y=8 
3x+8y=−16
Find the equation of the lines below, in standard form.
 slope = 2 and passes through (3, 5)
 slope
=−12 and passes through (6, 3).  passes through (5, 7) and (1, 2)
 passes through (5, 5) and (5, 3)
 Change
Ax+By=C into slopeintercept form.  From #16, what are the slope and
y− intercept equal to (in terms ofA,B, and/orC )?  Using #16 and #17, find one possible combination of
A,B, andC fory=12x−4 . Write your answer in standard form.  The measure of a road’s slope is called the grade. The grade of a road is measured in a percentage, for how many vertical feet the road rises or declines over 100 feet. For example, a road with a grade incline of 5% means that for every 100 horizontal feet the road rises 5 vertical feet. What is the slope of a road with a grade decline of 8%?
 The population of a small town in northern California gradually increases by about 50 people a year. In 2010, the population was 8500 people. Write an equation for the population of this city and find its estimated population in 2017.