Question

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.
2. Describe how you would graph this line using the slope-intercept method. Be sure to write
using complete sentences.
3. Write the equation in function notation. Explain what the graph of the function represents. Be
sure to use complete sentences.
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.

Answer 1

To change the equation to slope-intercept form, subtract 2x from both sides and divide everything by 3. The slope is -2/3 and the y-intercept is 490. The graph represents Sal's profit from lunch specials as a function of the number of sandwich lunch specials sold.

Step-by-step explanation:

To change the equation to slope-intercept form, we need to solve for y. First, subtract 2x from both sides of the equation, which gives us 3y = -2x + 1470. Then, divide everything by 3 to isolate y: y = (-2/3)x + 490. The slope of the equation is -2/3, and the y-intercept is 490.

To graph this line using the slope-intercept method, start by plotting the y-intercept at (0, 490). Then, use the slope (-2/3) to find the next point. Since the slope is negative, move down 2 units and right 3 units to plot the next point. Continue this process to plot more points, and then connect them to draw the line.

The equation in function notation is f(x) = (-2/3)x + 490. The graph of this function represents Sal's profit from lunch specials as a function of the number of sandwich lunch specials sold (x). It shows how the profit changes based on the number of sandwiches sold.

To graph the function, plot the y-intercept at (0, 490) and use the slope (-2/3) to find additional points. Connect these points to draw the line. Label the x-intercept as the number of sandwich lunch specials and the y-intercept as the profit from lunch specials.

Learn more about slope-intercept form of equations