Choose the graph that shows the solution to the system of inequalities

What is the equation of the line that passes through 1,4 and 2,1

sashaice [31]

Answer:

y = -3x + 7

Step-by-step explanation:

The equation of a line

y = mx + c

y - intercept point y

m - slope of the line

x - intercept point x

c - intercept point of the line

Step 1: find the slope

m = y2 - y1 / x2 - x1

Given two points

( 1 , 4) ( 2 , 1)

x1 = 1

y1 = 4

x2 = 2

y2 = 1

insert the values

m = 1 - 4 / 2 - 1

m = -3/1

m = -3

y = -3x + c

Step 2: substitute any of the two points given into the equation of a line

y = -3x + c

( 1 ,4)

x = 1

y = 4

4 = -3(1) + c

4 = -3 + c

4 + 3 = c

c = 7

Step 3: sub c into the equation

y = -3x + 7

The equation of the line is

y = -3x + 7

3 0

3 years ago

A school is organizing a weekend trip to a nature preserve. For each student, there is a $50 charge, which covers food and lodgi

k0ka [10]

The number of students going on the trip is 50.

Given,

A school is organizing a weekend trip to a nature preserve.

For each student, there is a $50 charge, which covers food and lodging. There is also a $25 charge per student for the bus.

The school must also pay a $15 cleaning fee for the bus.

The total cost of the weekend is $3,765.

We need to find out how many students will be going on the trip.

<h3>How do we find the number of items from the cost of each item and the total amount?</h3>

We simply divide the total cost by the cost of each item.

Example:

Total amount = 10

Each item cost = 2

Number of items = 10/2 = 5

Find the charge of each student.

= Food and lodging charge + bus charge

= $50 + $25

= $75

Find the additional charge for the trip.

= Cleaning charge

= $15

Find the total cost of the trip.

= $3,765

Find the total charge from the students.

= $3,765 - $15

= $3,750

Find the number of students who went on the trip.

= Total charge from the student's ÷ cost of each student

= 3750 ÷ 75

= 3750 / 75

= 50

This means 50 students.

Thus the number of students who went on the trip is 50.

Learn more about finding the number of students who like both games with a ratio given here:

brainly.com/question/24125573

#SPJ2

8 0

2 years ago

Read 2 more answers

What is the equation of this line x-3y=18 in slope intercept form

sergejj [24]

Y=3negativeX+18. y=3(-x)+18. I hope I helped.

3 0

3 years ago

A single story house is to be built on a rectangular lot 70 feet wide by 100 feet deep. The shorter side of the lot is along the

dedylja [7]

Answer:

250 sq ft

Step-by-step explanation:

Since the shorter side is along the street and the setback is 10ft from each side, the house is 50 ft wide

and 100 -20 -30 = 50 ft long

50 x 50 = 250 sq ft

3 0

3 years ago

PLEASE HELP ME!! I can’t figure this out

DochEvi [55]

Hello!

The problem has asked that we write a point-slope equation of the line in the image above. Point-Slope Form uses the following formula:

y – $y_{1}$ = m(x – $x_{1}$ )

In this case, M represents the slope while $X_{1}$ and $Y_{1}$ represent the corresponding X and Y values of any given point on the line.

We are given that the slope of the line is - $\frac{5}{7}$ . We also know that any given point on a graph takes the form (x,y). Based on the single point provided in the image above, we can determine that $X_{1}$ is equal to 6 and $Y_{1}$ is equal to 2. Now insert all known values into the point-slope formula above:

y – 2 = - $\frac{5}{7}$ (x – 6)

We have now successfully created an equation based on the information given in the problem above. Looking at the four possible options, we can now come to the conclusion that the answer is C.

I hope this helps!

7 0

3 years ago