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

Answer:

y = -2/3x + 300

Step-by-step 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).

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\m=\frac{300 -0 }{0 -450 }\\m=\frac{300}{-450} \\m=-\frac{2}{3}$

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