All categories

2 years ago

What is an equation of the line that passes through the points (3,4) and (−4,−3)? Put your answer in fully reduced form

Mathematics

1 answer:

sasho [114]2 years ago

3 0

Answer:

The equation of the line is y = x + 1

Step-by-step explanation:

The equation of the line is y = m x + b, where

m is the slope of the line

b is the y-intercept

The rule of the slope of the line is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (3, 4) and (-4, -3)

∴ x1 = 3 and y1 = 4

∴ x2 = -4 and y = -3

→ Substitute them in the rule of the slope above to find it

∵ m = $\frac{-3-4}{-4-3}$ = $\frac{-7}{-7}$ = 1

∴ m = 1

→ Substitute it in the form of the equation above

∴ y = 1(x) + b

∴ y = x + b

→ To find b substitute x by 3 and y by 4 in the equation

∵ 4 = 3 + b

→ Subtract 3 from both sides

∵ 4 - 3 = 3 - 3 + b

∴ 1 = b

→ Substitute it in the equation

∴ y = x + 1

∴ The equation of the line is y = x + 1

You might be interested in

Brainliest if correct

andrezito [222]

A to the sixth power

8 0

2 years ago

Read 2 more answers

Emily is giving candy to 8 of her friends. She wants to give each friend 2/3 of a chocolate bar. How many whole chocolate bars d

andrew11 [14]

Answer:

she needs 1/3 chocolate bars

Step-by-step explanation:

8 × 2/3

=5 1/3

7 0

2 years ago

A bag of rice weighs 3.18 pounds find the mass in kilograms

sleet_krkn [62]

Answer:
1kg=2.2lb
So,
3.18lb=3.18/2.2kg
1.44kg

7 0

3 years ago

bilogy a new flu virus is introdused when a stranger visits an isilated vilige of 8000 people. Every infected person infect 2 mo

kumpel [21]

Answer: u(n)=8000−3n⋅2

Step-by-step explanation:

Let i(n) be the number of infected people and u(n) the number of uninfected people, both on the n-th day.

Let x(n) be the number of people who got infected on the n-th day. The relation between i(n) and x(n) is given by:

i(n)=i(n−1)+x(n)

Let's assume the stranger leaves before the next day.

Taking the day the stranger arives as the 0-th day and assuming he infects two people on that day, then

i(0)=x(0)=2

u(0)=8000−2=7998

The two people infected now will also infect two other people, meaning that:

x(1)=2i(0)=4

i(1)=i(0)+x(1)=6

u(1)=7998−x(1)=7994=8000−i(1)

Some more relations become clear:

u(n)=u(n−1)−x(n)

u(n)=8000−i(n)

As every person infects two people per day, then

x(n)=2i(n−1)

Therefore

i(n)=i(n−1)+2i(n−1)=3i(n−1)

This a recurrence relation for the number of infected people at a given day:

i(n)={3i(n−1)

if n is not equal to 2

if n=0

Implies

i(1)=3i(0)=6=31⋅2

i(2)=3i(1)=18=32⋅2

i(3)=3i(2)=54=33⋅2

Analogously, we can figure out that

i(n)=3n⋅2

Hence the number of uninfected people on day n is

u(n)=8000−3n⋅2

3 0

2 years ago

A 26-by-27-inch sheet of paper is to be used for a poster, with the shorter side at the bottom. Find the width of the margins if

Kipish [7]

Answer:

Step-by-step explanation:

Let the width of the margins as x.

So, we subtract 'x' width on each side of the paper.

So, length = 26-x-x= 26-2 x

Width = 27-x-x=27-2 x

Now, it is given printed area is 360

We can set up equation using length x width = Area

(26-2 x)(27-2 x) = 360

Multiply the left side using FOIL method,

702 -52 x-54 x+4 x^2 =360

Combine like terms

702-106x+4x^2=360

Subtract both sides 360

4x^2-106x+342 =0

Let's divide both sides by 2 to simplify

2x^2 -53x+171=0

Let's use quadratic formula to solve.

I'll upload the file for this.

There are two possible values for x.

Approximately x= 22.46 , x=3.76

Here x=3.76 works b

6 0

3 years ago