Question

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.

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.

Answer 1

y = -2/3x + 300

Explanation:

Since the line is linear, we can find the equation of the line in y=mx+b form.

First, you have to find the slope using the slope formula. Pick two points from the graph and plug it into the equation. It doesn't matter which ones; you will get the right answer regardless. I picked the points (0, 300) and (450, 0).

`m=(y_(2) -y_(1) )/(x_(2) -x_(1) )\\m=(300 -0 )/(0 -450 )\\m=(300)/(-450) \\m=-(2)/(3)`

You now have slope (m). You have to find the y-intercept (b) next. The y-intercept is the point where the line crosses the y-axis. For this graph, the line crosses the y-axis at (0, 300), making the y-intercept 300.

Since you have m and b, you can plug the values into y=mx+b.

y = mx + b

y = -2/3x + 300