In order to determine which is the graph, write the given situation as a inequality. If x is the number of pound of tea and y the number of pounds of coffe, for x pounds of tea and y pounds of coffe, the cost is 16x + 8y.
Moreover, The restaurant owner can not spend more than $280. Then, the number of x pounds of tea and y pounds of coffe are given by the following inequality:
16x + 8y ≤ 280
solve the previous inequality for y, as follow:
16x + 8y ≤ 280 subtract 16x both sides
8y ≤ -16x + 280 divide by 8 both sides
y ≤ -2x + 35
The previous result means that the number of pounds of coffe must belower or equal than -2x + 35. The limit for the values of y is given by the following equation of the line:
y = -2x + 35
the y and x intercepts of the line are:
y-intercept:
y = -2(0) + 35 = 35
y = 35
x-intercept:
0 = -2x + 35
2x = 35
x = 35/2
x = 17.5
Form the given answer choices, you can notice that option B because this graph has the same x and y intercepts we have found.
