50 points! 1. The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money ONLY on ride tickets and fair admission. The price of the fair admission is the SAME for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Using the information provided for Jermaine, what is the price of the fair admission? Show all steps for full credit.

(b) Using the x and y as defined in the problem, write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.

Step 1: Identify the slope and y-intercept for the equation.

Step 2: Write the equation in slope-intercept form.

2. A line goes through the points (8,9) and (-2,4).
(a) What is the slope of the line? Show your work.

(b) Write the equation of the line in point-slope form. Show your work.

(c) Write the equation of the line in slope-intercept form. Show your work.

3. What are the x and y intercepts of the equation in Question 2 (copied below)? Please type them in ordered pair form and show your work.

A line goes through the points (8,9) and (-2,4) .

1.

(a) The variables are:

→ y is the total cost

→ x is the number of ride tickets

→ c is the price of the fair admission

(b) The linear equation that can be used to determine the cost for

anyone who only pays for ride tickets and fair admission is

y = 1.25 x + c

(c) Because the equation is linear which means the value of y depends on

the value of x and the value of c = 5 does not change so the equation

can be used to determine the cost for anyone who only pays for ride

tickets and fair admission

2.

(a) The slope of the line is \frac{3}{4}

4

3

(b) The equation of the line in point-slope form is:

y - 3 = \frac{3}{4}

4

3

(x + 4)

(c) The equation of the line in slope-intercept form is:

y = \frac{3}{4}

4

3

x + 6

3.

The inequality that model the problem is:

20x + 10y ≥ 2000

Step-by-step explanation:

1.

The given is:

1. The county fair charges $1.25 per ticket for the rides.

2. Jermaine bought 20 tickets for the rides and spent a total of $35.00

at the fair

3. Jermaine spent his money only on ride tickets and fair admission

4. The price of the fair admission is the same for everyone

Use y to represent the total cost and x to represent the number of

ride tickets

∵ The price of a ticket = $1.25

∵ The number of tickets = x

∵ y represents the total cost

∵ The total cost = the cost of a ticket × the number of tickets + the price

of the fair admission

∴ y = 1.25 x + c, where c is the fair admission

∵ Jermaine bought 20 tickets

∴ x = 20

∵ Jermaine spent a total of $35.00 at the fair

∴ y = 35

- Substitute these values in the equation in step b

∴ 35 = 1.25(20) + c

∴ 35 = 25 + c

- Subtract 25 from both sides

∴ c = 5

∵ c represents a constant term (y-intercept) in the linear equation

∴ The price of the fair admission for any one is $5

(a)

The variables are:

→ y is the total cost

→ x is the number of ride tickets

→ c is the price of the fair admission

(b)

The linear equation that can be used to determine the cost for

anyone who only pays for ride tickets and fair admission is

y = 1.25 x + 5

(c)

Because the equation is linear which means the value of y depends on

the value of x and the value of c = 5 does not change so the equation

can be used to determine the cost for anyone who only pays for ride

tickets and fair admission

2.

A line goes through the points (-4 , 3) and (4 , 9)

The rule of the slope of a line is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}m=

x

2

−x

1

y

2

−y

1

∵ x_{1}x

1

= -4 and x_{2}x

2

= 4

∵ y_{1}y

1

= 3 and y_{2}y

2

= 9

∴ m=\frac{9-3}{4--4}=\frac{6}{8}=\frac{3}{4}m=

4−−4

9−3

=

8

6

=

4

3

(a)

The slope of the line is \frac{3}{4}

4

3

(b)

The point-slope form of the equation is y-y_{1}=m(x-x_{1})y−y

1

=m(x−x

1

)

∵ y_{1}y

1

= 3 and x_{1}x

1

= -4

∵ m = \frac{3}{4}

4

3

∴ y - 3 = \frac{3}{4}

4

3

(x - -4)

∴ y - 3 = \frac{3}{4}

4

3

(x + 4)

The equation of the line in point-slope form is:

y - 3 = \frac{3}{4}

4

3

(x + 4)

(c)

The slope-intercept form of the equation is y = mx + c, where c is the

y-intercept

∵ m = \frac{3}{4}

4

3

∴ y = \frac{3}{4}

4

3

x + c

- To find c substitute x and y by the coordinates of one of the two

given points

∵ x and y are the coordinates of point (4 , 9)

∴ 9 = \frac{3}{4}

4

3

(4) + c

∴ 9 = 3 + c

- Subtract 3 from both sides

∴ c = 6

∴ y = \frac{3}{4}

4

3

x + 6

The equation of the line in slope-intercept form is:

y = \frac{3}{4}

4

3

x + 6

3.

Jacob and Sarah are saving money to go on a trip

The given is:

1. They need at least $2000 in order to go

2. Jacob mows lawns and Sarah walks dogs to raise money

3. Jacob charges $20 each time he mows a lawn and Sarah charges

$10 each time she walks a dog

4. x representing the number of lawns mowed and y representing the

number of dogs walked

∵ x representing the number of lawns mowed

∵ Jacob charges $20 each time he mows a lawn

∴ Jacob can earn $20x

∵ y representing the number of dogs walked

∵ Sarah charges $10 each time she walks a dog

∴ Sarah can earn 10y

∵ They need at least $2000 in order to go to the trip

∴ 20x + 10y ≥ 2000

The inequality that model the problem is:

20x + 10y ≥ 2000

Learn more:

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step-by-step explanation: