In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, David has scored 81, 92, and 74 on the first three. What range of scores on the fourth test will give David a B for the semester (an average between 80 and 89, inclusive)?Assume that all test scores have a non-negative value.
Express your answer in interval notation.

The answer in interval notation is ( 73 ,  100 )

Step-by-step explanation:

If we call x and y the lower and upper values for David to get an average of 80 and 89 respectively, we can calculate these two values solving a pair of equations:

(81  +  92  + 74  +  x ) / 4  = 80     ⇒   (247  +  x  )/4 = 80

247  +  x  =  320    ⇒    x  =  320 - 247

x  =  73

And

(81  +  92  + 74  +  y ) / 4  = 89     ⇒   ( 247  +  y ) / 4  =  89

247   +  y  =   356

y  =  356  -  247

y  =  109

But tests are a 100-point test

Then the answer in interval notation is ( 73 ,  100 )

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is