Luis and Raul are riding their bicycles to the beach from their respective homes. Luis proposes that they leave their respective homes at the same time and plan to arrive at the beach at the same time. The diagram shows​ Luis's position at two points during his ride to the beach. Write an equation in​ slope-intercept form to represent​ Luis's ride from his house to the beach. If Raul lives 5 miles closer to the beach than​ Luis, at what speed must Raul ride for the plan to​ work?


If x represents the time in hours since the ride began and y represents the remaining distance from the​ beach, then the equation

_____



represents​ Luis's ride from his house to the beach.

Answer:

equation: y=-7.5x+15 and Raul must ride at a speed of 5 mi/hr

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}[/tex] to find out the slope. [tex]\frac{6-11.25}{1.2-0.5}[/tex]=[tex]\frac{-5.25}{0.7} = -7.5[/tex]

Then you fill x and y to find out the y intercept

[tex]11.25=-7.5*0.5+b[/tex]

[tex]11.25=-3.75+b\\11.25+3.75=15\\[/tex]

Y intercept= 15

then you put it in the equation:

y=-7.5x+15

Since Raul lives 5 miles closer and Luis is 5 miles away, he needs to go at 5 miles an hour to get to the spot.

That is 5 miles/hour

The distance and time, as presented in this question are illustrations of linear equations.

From the diagram, we have:

[tex](x_1,y_1) = (0.5,11.25)[/tex]

[tex](x_2,y_2) = (1.2,6)[/tex]

Start by calculating the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{6 - 11.25}{1.2 - 0.5}[/tex]

[tex]m = \frac{-5.25}{0.7}[/tex]

[tex]m = -7.5[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives

[tex]y = -7.5(x - 0.5) + 11.25[/tex]

[tex]y = -7.5x + 3.75 + 11.25[/tex]

[tex]y = -7.5x + 15[/tex]

Calculate distance, when [tex]x = 5[/tex]

We have:

[tex]y = -7.5 \times 5 + 15[/tex]

[tex]y = -22.5[/tex]

The speed (s) is then calculated as:

[tex]s = \frac{22.5}{5}[/tex]

[tex]s = 4.5[/tex]

Hence, he must plan to ride at 4.5 miles per hour

Read more about linear equations at:

https://brainly.com/question/11897796

A bakery has 72 half gallons of milk. It takes 1 2/3 cups of milk to make a cake. Note that 1 cup = 1/8 half gallon = 0.125 half gallon. How many cakes can the bakery make?

A. 43 cakes
B. 288 cakes
C. 345 cakes
D. 576 cakes

At the park, a statue stands on a marble base. The statue and marble base have a total height of 59.4 inches. The height of the marble base is 16.09 centimeters. Given that 1 inch is equal to 2.54 centimeters, what is the height of the statue?

Which is an equation of a line with a slope of 1/2 that contains the point (-4,7)?

Based on the number line below, which statement is true?

Help!!!!!!!!!!!!!!!!

What is the value of (-5) the power of 4

solve -x/3 > 5

a) x -15

c) x 15

If I deposit $1500 in my bank account and it increased by 15% at the end
of the year, how much money is now in my bank account

Multiply: (3x + 2)(4x + 2)
07x2 + 12 x+4
12 x2 + 14 x+4
33+4x+ 2
12 x2 + 18 x+2

Multi Step Problem (Show work!!)

Y + 7 = -2​

Is 0.819 meters greater than 0.85 meters and why

Is 59 - - 2 positive or negative?

Find the interest for the given dates to the nearest cent. 6,150 dollars at 9% for 12/5 to 12/30 Please help! :)

Write equation of the circle with center c(-1, 5) and radius 3

Given f(x) = 3x - 4, find f(5). Write your answer as a number.​

1 week away from the election. Who do you think wins? Why do you think so? Who do you want to win? Who is better for the country? Why??? (Trump 2020)

Is anyone a disgrace to their parents

what is 2+2x 100000000000 +5 /10

Solve the system of equations using substitution.
- 4x + 4y= 8
y= -2x – 10
-
O (4, -18)
O (12, -34)
o(-4,-2)
O (-2,-6)

PLEASE HELP I AM BEING TIMED!!!

Statment: Find the measure of the angle indicated by 19x+5

Options: 130
50
80
100

Paul gets money for each chore he completes around the house. He receives $5.00 for taking out the garbage all week, $10.00 for cleaning the bathroom, $3.00 for each time he empties the dishwasher, and $4.00 an hour for babysitting his younger sister. This week, he took out the garbage, emptied the dishwasher three times, and babysat his sister for five hours. How much money should he receive?

Lois Lane leaves Metropolis driving 50 km/h. Three hours later, Superman leaves Metropolis to catch up to her, flying at 300 km/h.

When does Superman catch up with Lois?

Superman will catch up ____ hours after Lois left Metropolis.

3/4x + 2 = 4 2/3
please help me with this!!

(04.05)Erika calculated that she would spend $115 on school supplies this year. She actually spent $82.50 on school supplies. What is Erika’s percent of error?

28.3%
2.8%
39.4%
32.5%

42.564in expanded form

What does the y-intercept represent in this scenario?

7a-3(2a-4) what’s the answer?

Which statement BEST describes the equation below?
f(x) = 2x + 3

A) It is a relation
B) It is a function
C) It is a one-to-one function

11. What is the difference between a theorem and a postulate?

Hint: Use the number line to find the missing value.
-2=_______+6

Solve for x. Show your work: x + 3 = 12