Kelly is going two work two part-time jobs during the school year. When she works for her dad, she will make $8.00 per hour. When she works at a day care center, she will make $14.00 per hour. To pay her car payment, Kelly needs to make at least $84.00 a week and can work no more than 10 hours total per week. Write an inequality to represent the difference combinations of hours working for her dad, X, and hours working for the daycare center, Y, Kelly can work if she wants to earn at least $84 per week

The answer is below

Step-by-step explanation:

Let x represent the number of hours Kelly works for her dad per week and y represent the number of hours Kelly works in the daycare center per week.

Since she wants to make $84 per week, hence:

8x + 14y ≥ 84     (1)

Also, she can work a maximum of 10 hours per week, hence:

x + y ≤ 10           (2)

Using equation 1 and 2 and plotting the constraints on geogebra online graphing tool, the solution to the problem is at points:

A(0, 6), B(0, 10) and C(9.3, 0.7)

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