Mathematics High School

Equation of the Line
Lesson
I
After going through this lesson, you are expected to find the equation of a
line given (a) two points, (b) the slope and a point and (c) the slope and its
intercepts
From the given linear equation, we can determine 2 points that will satis-
fy the equation. Also we can determine the slope and the y- intercept so as the
x and y intercepts.
Example: Given - 2x + y = 6
Find: a. two points that will satisfy the equation
(b) slope and y-intercept
(c) x and y intercept
Solution:
(a) -2x + y = 6
If x = -1
If y = 2
-21-1) + y = 6
- 2x + 2 = 6
2 + y = 6- y = 4
-2x = 4-x= -2
The point is (-1,4)
The point is (-2, 2)
(b) Change the equation to slope intercept form : y = 2x + 6
Therefore the slope m = 2 and the y-intercept b = 6
(c) Find the and y intercept of -2x + y = 6
Let x = 0, -2(0) + y = 6; y = 6. the intercept is (0,6)
Let y = 0, -2x + 0 = 6; -2x = 6, X = -3, the y intercept is (-3,0)
Learning Task 1 : From the given equation of the line a) find two points that will
satisfy the equation, b) the slope and the y intercepts and c) the x and y-
intercepts.
2.
3y - X9
1. 3x + 2y = 5

Answers

Answer 1

9514 1404 393

Answer:

a) (0, 5/2), (5/3, 0)

b) m = -3/2; b = 5/2

c) (5/3, 0), (0, 5/2)

Step-by-step explanation:

Given:

3x +2y = 5

Find:

a) two points that satisfy the equation

b) slope and y-intercept

c) x-intercept

Solution:

Since the intercepts are points on the line, finding them satisfies all parts of the question except finding the slope.

a) Let x=0. Then we can find y from ...

3·0 +2y = 5

y = 5/2

One point is (0, 5/2).

Let y=0. Then we can find x from ...

3x +2·0 = 5

x = 5/3

Another point is (5/3, 0).

Two points on the line are (0, 5/2) and (5/3, 0).

b) The slope can be found using the slope formula on the two points we found.

m = (y2 -y1)/(x2 -x1)

m = (0 -5/2)/(5/3 -0) = -(5/2)/(5/3) = -3/2

The slope is -3/2. The y-intercept is 5/2.

c) The x- and y-intercepts are (5/3, 0) and (0, 5/2), respectively.

Equation Of The LineLessonIAfter Going Through This Lesson, You Are Expected To Find The Equation Of

Related Questions

Chase wants to earn at least $900 this month in commission. What is the minimum amount he needs to sell in order to earn $900 if he earns a 3.3% commission on everything he sells? Round to the nearest dollar.

Answers

Answer:

$27,272.73= sales

Step-by-step explanation:

Giving the following information:

Desired commission= $900

Commission rate= 3.3% = 0.033 of sales

To calculate the sales required, we need to use the following formula:

Commission= sales*commission rate

900= sales*0.033

900/0.033= sales

$27,272.73= sales

Answer: $27,273

Step-by-step explanation: 900a=3.3100 Write the proportion. Let a represent the amount he needs to sell.

900a=3.3100 Because 3.3×272.72=900 , multiply 100 by 272.72 to find a.

90027.271=3.3100 100 × 272.72 ≈ 27,273, so a = 27,273.

Chase needs to sell $27,273 to earn $900 in commission.

Which of the following relations describes a function?
OA. {(-3,-4), (-4,-3), (3, 4), (4,3)}
OB. {(3,-1), (3, 1), (4, -1), (4, 1) }
OC. {(3, 3), (3, 4), (4,3), (4,4)}
OD. {(0,0), (0, 3), (3, 0), (3, 3) }

Answers

Answer:

{(-3,-4), (-4,-3), (3, 4), (4,3)}

Step-by-step explanation:

{(-3,-4), (-4,-3), (3, 4), (4,3)}

because x should not be the same in more than one pair

Is this set of ordered pairs a function ? (1,9) (0,8) (3,0) (4,9) (7,7).

Answers

Answer:

It is not a function because the output of 9 repeats.

(1,9) (4,9)

How many terms are in the expression 4x2 + y - 0 ?
help pleaseeee

Answers

Answer:

3 I did the test to btw

Step-by-step explanation:

did the test

help anyone?? PLSS ?? ill love u 4eva

Answers

Answer:

4 and 5

Step-by-step explanation:

xy = 20

x + y = 9 ⇒ x = 9 - y

y(9 - y) = 20

9y - y² = 20

y² - 9y + 20 = 0

D = ( - 9)² - 4(1)(20) = 81 - 80 = 1

[tex]y_{1}[/tex] = (9 + 1) ÷ 2 = 5

[tex]y_{2}[/tex] = (9 - 1) ÷ 2 = 4

The numbers are 4 and 5

Write 12 1/3 as an improper fraction.

Answers

Answer: 37/3

Step-by-step explanation:

12 1/3 = 12*3+1/3 = 37/3

Answer:

[tex]\frac{37}{3}[/tex]

Step-by-step explanation:

[tex]12\frac{1}{3}[/tex]

When converting mixed numbers (such as the one above), to improper fractions, we must first multiply the whole number by the denominator:

[tex]12*3=36[/tex]

Then, add the numerator the the product:

[tex]36+1=37[/tex]

Now, put the sum over the denominator to get your solution:

[tex]\frac{37}{3}[/tex]

To check your work, you can convert the improper fraction to a mixed number to make sure you will end up with [tex]12\frac{1}{3}[/tex].

Divide [tex]37[/tex] into [tex]3[/tex]:

[tex]12[/tex] with a remainder of [tex]1[/tex]

Put the remainder over the denominator:

[tex]12\frac{1}{3}[/tex]

Therefore, our solution is correct!

Savannah and Reagan both work in a grocery store. They each stocked the same number of shelves last Saturday, but it took Reagan less time. They've been told that they'll spend their entire 4-hour shifts next Saturday stocking shelves. If their average speeds are consistent, who will likely stock more shelves next Saturday?

HELP!

Answers

Answer:

Reagan

Explanation:

Since Reagan is able to stock the same number of shelves as Savannah while spending less time to do so, it means that Reagan is able to stock shelves faster than Savannah, thus Reagan is able to stock more shelves than Savannah given that their average speeds are constant and that they both work under 4-hour shifts.

Hope this helps :)

Help!! Please and thank you

Answers

Answer:

110.9 cm³

Step-by-step explanation:

[tex]V=\frac13\cdot A_b\cdot H[/tex]

[tex]A_b[/tex] - Base Area

H - Height of the pyramid

Base is regular triangle: [tex]A_b=\dfrac{8^2\sqrt3}4[/tex]

The volume:

[tex]V=\dfrac13\times \dfrac{8^2\sqrt3}4\times 12=64\sqrt3\approx110.9[/tex]

A container has 12 1/2 cups of pancake mix. A serving uses exactly 1 1/2
cups
• How many full servings are in the container?
• How many cups of pancake mix are left over?
Enter each answer on a separate line.

Answers

Answer:

8 full servings

Step-by-step explanation:

1/2 cup of mix left

Will mark Brianliest answer correctly !!!!!!!!!! Pleaseeee helpppp !!!!!!!!!!!!!!!!!

Answers

it would be 2 Square root 10

2 is the square root of 10

Factorise the expression 6x^2-13x+6 and hence solve the equation 6x^2-13x+6=0

Answers

Answer:

Part A

The factored form of the expression, 6·x² - 13·x + 6 is (2·x - 3) × (3·x - 2)

Part B

The solution of the equation 6·x² - 13·x + 6 = 0 are x = 3/2 or x = 2/3

Step-by-step explanation:

Part A

The given expression to factorize is 6·x² - 13·x + 6, which can be written as follows;

6·x² - 13·x + 6 = 6·x² - 4·x - 9·x + 6

The 13·x is split at - 4·x - 9·x

6·x² - 4·x - 9·x + 6

2·x·(3·x -2) - 3·(3·x - 2)

Bringing out the common factor (3·x - 2) gives;

(2·x - 3) × (3·x - 2)

Therefore, the expression 6·x² - 13·x + 6 in factored form is (2·x - 3) × (3·x - 2)

Part B

Solving the equation, 6·x² - 13·x + 6 = 0, therefore gives;

6·x² - 13·x + 6 = (2·x - 3) × (3·x - 2) = 0

Therefore, either (2·x - 3) = 0 and x = 3/2 or (3·x - 2) = 0 and x = 2/3

From which we have 6·x² - 13·x + 6 = 0 when x = 3/2 or 2/3 and x = 3/2 or x = 2/3 are the solution of the equation 6·x² - 13·x + 6 = 0.

1. There are 6 fewer books in Ashley’s library than Jennifer’s. If there are 30 books total, how many books does Ashley have?
a. 16 b. 10 c. 18 d. 12

Answers

It’s C because Jennifer has 18 whole Ashley has 12 which adds up to 30.

Use long division to calculate 276 ÷ 15

Answers

Answer:

18.4

Step-by-step explanation:

Which function represents the sequence -5.5, -4.75 -4,-3.25... ?

Answers

The answer I think should be
C main

Find y.
A. 6
B.2
C.7
D.4

Answers

Answer: HOPE THIS HELPS GOD BLESS PLEASE TOUCH THANKS

C.8

Step-by-step explanation:

(5, 4) (7,10)
find the slope

Answers

Answer:

Step-by-step explanation:

The difference between the y coordinates is 6.

The difference between the x coordinates is 2

The slope is rise over run so in this case, the rise is 6 and the run is 2.

This makes our slope:

6/2

This can be simplified to 3/1 so the slope is 3.

For the function y = 4x – 2, what is the value of the function when x is equal to -3?

Answers

y= -14 !!! positive

Answer:

the value of y would be -14

Which of the following shapes are congruent?

Answers

Answer:

2nd option.............................................

Ricardo open a savings account with an initial deposit of $560 and will not make any additional deposits or withdrawals . The account earns 1% simple interest. What is the total amount that Ricardo will have in his account at the end of 3 years ?
A:$168.00
B:$56.00
C:$576.80
D:$565.60

Answers

Answer:

Step-by-step explanation:

How many tables that seat eight are required to provide places for 62 people at a banquet

Answers

Answer:

Step-by-step explanation:

62 divided by 8 is 7.75

you can't cut people so round it up and you get 8

Is 18x-2y = 26 linear or non linear?

Answers

Answer: it’s a linear function

Step-by-step explanation:

18x-2y=26 as -2y= -18x + 26 by adding 18x to both sides, and then y=9x - 13 by dividing both sides by -2. So, it represents a linear function

Answer:

It's linear

Step-by-step explanation:

18x-2y=26

Because it has two variables x and y

In a game of spinning wheels, Ann got to spin a wheel twice. She scored –50 points for the first spin and 90 points for the second spin. If her score at the beginning was zero, then what would be her total score after the two spins?

Answers

Answer:

Step-by-step explanation:

-50 + 90 = 40

Write the equation of the line in slope intercept form that passes through the point (6, -1) and has a slope of -2.

Answers

Answer:

Y=6X-32

Step-by-step explanation:

Answer:

y-y1=m(x-x1)

y-6=-2(x-(-1))

y-6=-2(x+1)

y-6=-2x-2

y=-2x+4

Step-by-step explanation:

One angle is five degrees less than three times the degree measure of another angle. Together, the angles measures have a sum of 143°. What is the measure of each angle?

Answers

Answer:

Step-by-step explanation:

B
1
N
4
5
5
(4x+6)
(5x -5)
7
00
0
A
С
(3x + 8)
The value of x is
and the length of the base is

Answers

Answer:

(4x+6)

(5x -5)

(3x + 8)

The value of x is