1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mkey [24]
3 years ago
10

Graph each linear equation that passes through the given pair of points. Use graph paper.

Mathematics
1 answer:
Naya [18.7K]3 years ago
6 0

Answer:

The easier way to solve this is to find the two points in the coordinate axis, and just draw a line that passes through the two points.

But let's be more complete:

Let's find the equations for each line:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

1) Here the points are (2,2) and (4,5)

then the slope is:

a = (5 - 2)/(4 - 2) = 3/2

y = (3/2)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (2, 2)

2 = (3/2)*2 + b

2 = 3 + b

2 - 3 = b

-1 = b

y = (3/2)*x - 1

2) Here the points are (0,1/2) and (2,3/2)

then the slope is:

a = (3/2 - 1/2)/(2 - 0) = 1/2

y = (1/2)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (0, 1/2)

1/2 = (1/2)*0 + b

1/2 = b

y = (1/2)*x + 1/2

3) Here the points are (-1,2) and (5,0)

then the slope is:

a = (0 - 2)/(5 + 1) = -1/3

y = (-1/3)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-1, 2)

2 = (-1/3)*-1 + b

2 = 1/3 + b

2 - 1/3 = b

5/3 = b

y = (-1/3)*x + 5/3

4) Here the points are (-5,-3) and (-3,5)

then the slope is:

a = (5 + 3)/(-3 + 5) = -4

y = -4*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-3, 5)

5 = -4*-3 + b

5 = 12 + b

5 - 12 = b

-7 = b

y = -4*x - 7

Now that we have all the equations, we can find the graphs.

where the colors are:

(4) green

(3) orange

(2) Blue

(1) Gray.

You might be interested in
Write an equation in slope intercept form for the line with slope of 1/5 and y-intercept -8
AlladinOne [14]

Answer:

y = (1/5)x - 8

Step-by-step explanation:

It's slope-intercept form y=mx+b and we just substitute m=1/5, b= -8.

8 0
3 years ago
Read 2 more answers
What is the solution of the system? Use substitution.
nekit [7.7K]
Substituting y=6x+2 into equation 3y - 18x =12 looks like:

3(6x + 2) - 18x = 12
18x + 6 - 18x = 12  distributive property left side
6 = 12  simplifying the left side

We now see a contradiction:   6 does not equal 12  What this tells us is that there is no solutions to this equation.  So choice 'C' ...
8 0
3 years ago
Read 2 more answers
Multiply. Write in simplest form. 1/2 * 24
Dennis_Churaev [7]

Answer:

1. 12

2. 4

3. 6.8

4. 4.5

5 1.2

Step-by-step explanation:

5 0
3 years ago
3,6,11,18,27,38
MakcuM [25]

Answer:  The pattern is x^2+2

where x is the term number

Example: the 5th term is 27 because x = 5 leads to x^2+2 = 5^2+2 = 27

=================================================

Explanation:

  • The jump from 3 to 6 is +3
  • The jump from 6 to 11 is +5
  • The jump from 11 to 18 is +7
  • The jump from 18 to 27 is +9
  • The jump from 27 to 38 is +11

The pattern of jumps is: 3, 5, 7, 9, 11

Those increments are going up by 2 each time.

Since we have a consistent pattern of increments, this means that the sequence follows a quadratic model.

Quadratics are stuff like x^2+7x+10 or 3x^2-7. The leading term has an exponent of 2.

-----------

If x is the term number and y is the term itself, then we have these points

(1,3)

(2,6)

(3,11)

(4,18)

(5,27)

(6,38)

The x coordinates increase by 1 each time. The y coordinates are the terms given by your teacher.

Pick exactly 3 of those points. I'll pick the first 3.

Why 3? Because we'll have 3 unknowns to solve for, in which we'll need 3 equations.

  • Plug (x,y) = (1,3) into y = ax^2+bx+c, then simplify. You should get the equation a+b+c = 3
  • Repeat for (x,y) = (2,6) and you should get 4a+2b+c = 6
  • Repeat for (x,y) = (3,11) and you should get 9a+3b+c = 11

-----------

We have this system of equations

\begin{cases}a+b+c = 3\\ 4a+2b+c = 6\\9a+3b+c = 11\end{cases}

There are a number of methods to solve this system. Substitution is what I'll go for.

Solve the first equation for c

a+b+c = 3

c = 3-a-b

Then use substitution.

4a+2b+c = 6

4a+2b+(3-a-b) = 6

3a+b+3 = 6

3a+b = 6-3

3a+b = 3

and

9a+3b+c = 11

9a+3b+(3-a-b) = 11

8a+2b + 3 = 11

8a+2b = 11-3

8a+2b = 8

We now have this reduced system of equations.

\begin{cases}3a+b = 3\\8a+2b = 8\end{cases}

I'll skip the steps as this solution is getting very lengthy as it is. The basic idea is to use substitution again. You should find that a = 1 and b = 0 form the solution set here.

Use those values to find c

c = 3-a-b

c = 3-1-0

c = 2

-----------

To summarize the previous section, we have these solutions:

a = 1, b = 0, c = 2

Therefore the equation y = ax^2+bx+c becomes y = 1x^2+0x+2 aka y = x^2+2. This lets us find any term.

Let's test it out.

  • If x = 1, then y = x^2+2 = 1^2+2 = 3
  • If x = 2, then y = x^2+2 = 2^2+2 = 6
  • If x = 3, then y = x^2+2 = 3^2+2 = 11

And so on. I'll let you test the other x values (4 through 6).

Another way to confirm the answer is to subtract 2 from each item in the original set {3,6,11,18,27,38} and you'll end up with {1,4,9,16,25,36}. This is the list of perfect squares. It shows that term x is simply x^2 but add on 2 so things are adjusted accordingly.

Side note: you can use a tool like GeoGebra or WolframAlpha to quickly solve the system of equations. However, I recommend it only as a means to check your answer rather than do the work for you.

7 0
2 years ago
A baseball player reaches first base 30% of the time he is at bat.out of 50 times at bat,about how many times will the player re
SOVA2 [1]

Answer:

15 times

Step-by-step explanation:

If he bats 50 times, he will be expected to reach first base "30% of the time".

We simply need to find "what is 30% of 50?"

We first need to convert the percentage (30%) to decimal and then multiply that with 50 to get our answer.

Converting percentage to decimal is very simple! We divide by 100. That's it!

So, we have:

30% = 30/100 = 0.3

Now we do the multiplication:

0.3 * 50 = 15

So, the player would reach first base 15 times (out of 50 times of batting)

6 0
3 years ago
Other questions:
  • -3s -5=4 what is this problem
    9·2 answers
  • (X^-3)^2(x^-2)^3 <br> PLS SIMPLIFY?!!!
    5·1 answer
  • PLEASE ANSWER AND EXPLAIN | 98 POINTS
    7·2 answers
  • Solve the following equation. 3x/7-2=15 (Must be a mixed number)
    11·1 answer
  • (1.)
    9·2 answers
  • is (3,-3) a solution to the system 5x+4y=3, 2x-5y=19 need to be taught step by step please and thank you.
    9·2 answers
  • in baseball anthony hit 0.63 of the pitches thrown at him what percent of the pitches did anthony miss
    12·1 answer
  • A train is exactly 24km from Smalltown at 7:00p.m. It travels toward Smalltown at a constant rate of 90km per hour. At what time
    11·1 answer
  • Which equation results from adding the equations in this system? 11 x minus 3 y = negative 17. Negative 4 x + 3 y = negative 18.
    13·1 answer
  • Tom was measuring a piece of wood to build a shelf for his daughter. The shelf is 36 inches long. He tells his daughter, Hadlee
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!