Project Option 1—Individually
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch
specials. The profit on every sandwich is $2, and the profit on every
wrap is $3. Sal made a profit of $1,470 from lunch specials last month.
The equation 2x + 3y = 1,470 represents Sal's profits last month, where
x is the number of sandwich lunch specials sold and y is the number of
wrap lunch specials sold.
1. Change the equation to slope-intercept form. Identify the slope
and y-intercept of the equation. Be sure to show all your work.
2x + 3y = 1,470
2x - 2x + 3y = 1470 - 2x
3y = -2x + 1470
3y/3 = (2x + 1470)/3
y = -2x/3 + 490
y = -2/3x + 490
-2/3 is the slope, 490 is the y-intercept.
2. Describe how you would graph this line using the slope-intercept
method. Be sure to write using complete sentences.
I would put the 490 for the y-intercept and put x = 0. That makes it (0,
490). Then I start at the 490 and find a different point by using the
slope, which is –2/3x. I do rise over run (which is y over x). But in this
case, there is a negative, so you go down –2 instead of up. Next, you go
right 3. That gives you the point (135, 400). Then, I connect the points
by using a straight line.
3. Write the equation in function notation. Explain what the graph of
the function represents. Be sure to use complete sentences.
f(x) = -2/3x + 490
The graph of the function represents the sandwich price and wrap price.
It also shows how many wraps were sold (490).
4. Graph the function. On the graph, make sure to label the
intercepts. You may graph your equation by hand on a piece of
paper and scan your work or you may use graphing technology.
5. Suppose Sal's total profit on lunch specials for the next month is
$1,593. The profit amounts are the same: $2 for each sandwich
and $3 for each wrap. In a paragraph of at least three complete
sentences, explain how the graphs of the functions for the two
months are similar and how they are different.
They are similar because they have the same slope, which is -2/3x. They
also both have negative linear lines. They are also similar because they
are both parallel to each other.
They are different because they have different y-intercepts. The old
equation has a y-intercept of 490, and the new equation has a yintercept of 531. They are also different because the newer equation
shows that there were more wraps sold than the first one. The newer
equation is 41 points above the first one. (531 – 490 = 41).
GRAPH WITH BOTH EQUATIONS:
02.03 Key Features of Linear Functions—Option 1 Rubric
Requirements
Student changes equation to
slope-intercept form. Student
shows all work and identifies the
slope and y-intercept of the
equation.
Student writes a description,
which is clear, precise, and
correct, of how to graph the line
using the slope-intercept
method.
Student changes equation to
function notation. Student
explains clearly what the graph of
the equation represents.
Student graphs the equation and
labels the intercepts correctly.
Student writes at least three
sentences explaining how the
graphs of the two equations are
the same and how they are
different.
Possible Points
4
4
4
4
4
Student Points