We are asked to find the linear function that represents the cost y for any number of samples x. The desired linear function has to follow a specific format.
y= mx+ b
For an equation in this form, m is the slope and b is the y-intercept. To find the desired linear function we will calculate the slope and the y-intercept. We can do this by using any two points lying on the line that is the graph of the linear function. Let's go through the content of the exercise and get the points we need!
Sentence From the Exercise
Point (x,y)
Admission and 3 samples cost $ 5.75.
( 3, 5.75)
Admission and 6 samples cost $ 8.75.
( 6, 8.75)
Now we can use the obtained points to calculate m. We will start by substituting the points into the Slope Formula.
In our function, a slope of 1 means that each sample of food costs $ 1. Now that we know the slope, we can write a partial version of the equation.
y= 1 x+ b
To complete the equation, we also need to determine the y-intercept b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 3, 5.75).
A y-intercept of 2.75 means that admission costs $ 2.75. We can now complete the equation.
y= 1x+ 2.75 ⇔ y =x+2.75
Therefore, A is the correct option.
