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.
The equation can be rewritten in the slope intercept form by making y the subject of the formula: 2x+3y= 1,470 or 3y=-2x+1,470 or y= -⅔ x + 490. Thus, for the given function: slope is -⅔ and y-intercept is 490.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
To graph the line using the slope intercept form, first mark out the y-intercept which is the point at which y is 0, i. e. when y=0, x= 735. Thus, the x-intercept is (735, 0) Thirdly, join the two points.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
The equation using a function is given by: f(x) = -⅔ x + 490. The graph of the function represents the number of sandwich lunch specials sold and the number of wrap lunch specials sold last week.
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.
The graph of the equation is attached.
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.
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. Then, the graph of the functions for the two months will have the same slope. The graph of the functions for the two months will be parallel. The graph of the functions for the two months will have different intercepts.
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.
Given a graph with intercepts (0,300) and (450,0). Recall that the equation of a line given two points: (x1,y1) and (x2,y2) is given by: y-300/x-0 = 0-300/450-0 450(y-300)=-300x 300x+450y=135,000 2x+3y=900. Therefore, the equation of the given line is 2x+3y=900.