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alina1380 [7]
3 years ago
8

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. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. 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. 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. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations. graph of line going through ordered pairs (0, 300) and (450, 0)

Mathematics
1 answer:
coldgirl [10]3 years ago
6 0
Changing the equation into slope form: y = mx + c, where m is the slope [gradient] and c is the y-intercept.

2x+3y=1470
3y = -2x+1470
y= - \frac{2}{3}x+ \frac{1470}{3}
y=- \frac{2}{3}x+490

The gradient is - \frac{2}{3} and y-intercept is at y=490

Graphing y=- \frac{2}{3}x+490 using slope-intercept method:
a) The slope is a negative slope. The line will go 'down hill'
b) The line must pass the point (0, 490)
c) The line will intercept the x-axis at y = 0
    0 = - \frac{2}{3}x+490
    \frac{2}{3}x = 490
    2x = 1470
    x = \frac{1470}{2}
    x = 735
    So, x-intercept is at (735, 0)

The graph of this function is shown below. The intercepts are labelled at:
y = 490
x = 735

-----------------------------------------------------------------------------------------------------------

Next month's profit equation

2x+3y=1593

Rewriting this into slope-equation form

3y = -2x+1593
y=- \frac{2}{3}+ \frac{1593}{3}
y= - \frac{2}{3}+531

The gradient, m, equals to - \frac{2}{3}
The y-intercept, c, equals to 531

The equation still has the same gradient with last month's profit equation but different y-intercept. 

-------------------------------------------------------------------------------------------------------------

A linear graph show points of (0, 300) and (450, 0)

We work out the slope: 
\frac{300-0}{0-450} = \frac{300}{-450}=- \frac{20}{30}  =- \frac{2}{3}


Y-intercept at x = 0, so it's at y = 300

Equation y = - \frac{2}{3}+300

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