<em> </em><u><em>SOLVING QUESTIONS FROM 1ST PAGE</em></u>
y = -3x - 5
Putting x = -5, and y = 0 in y = -3x - 5
0 = -3(-5) - 5
0 = 15 - 5
0 = 10 ∵Putting B(-5, 0) in y = -3x - 5 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
- Given the point C<em>(-2, 1)</em>
y = -3x - 5
Putting x = -2, and y = 1 in y = -3x - 5
1 = -3(-2) - 5
1 = 6 - 5
1 = 1 ∵Putting C(-2, 1) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
- Given the point D<em>(-1, -2)</em>
y = -3x - 5
Putting x = -1, and y = -2 in y = -3x - 5
-2 = -3(-1) - 5
-2 = 3 - 5
-2 = -2 ∵Putting D(-1, -2) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
<em> </em><u><em>SOLVING QUESTIONS FROM 2ND PAGE</em></u>
y = -2x + 18
Putting x = 6, and y = 18 in y = -2x + 18
18 = -2(6) + 18
18 = -12 + 18
18 = 6 ∵Putting B(6, 18) in y = -2x + 18 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
y = 2x + 6
Putting x = 9, and y = 24 in y = 2x + 6
24 = 2(9) + 6
24 = 18 + 6
24 = 24 ∵Putting C(9, 24) in y = 2x + 6 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
<em> </em><u><em>SOLVING QUESTIONS FROM 3RD PAGE</em></u>
y = 3x + 4
Putting x = 2, and y = 7 in y = 3x + 4
7 = 3(2) + 4
7 = 6 + 4
7 = 10 ∵Putting D(2, 7) in y = 3x + 4 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
<em> </em><u><em>SOLVING QUESTIONS FROM 4th PAGE</em></u>
<em>b. Which function could have produced the values in the table.</em>
<em>A. y = 3x + 4 </em>
<em>B. y = -2x + 18</em>
<em>C. y = 2x + 6</em>
<em>D. y = x + 9</em>
<em>The Table:</em>
<em>x y</em>
3 12
6 18
9 24
<em>Checking A) y = 3x + 4</em>
<em>Putting (3, 12), (6, 18) and (9, 24) in y = 3x + 4</em>
For (3, 12)
y = 3x + 4
12 = 3(3) + 4
<em>12 = 13 </em>∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (6, 18)
18 = 3(6) + 4
18 = 18 + 4
<em>18 = 22 </em>∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (9, 24)
24 = 3(9) + 4
24 = 27 + 4
<em>24 = 31 </em>∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
So, the equation y = 3x + 4 could have not produced the all values in the table as the the ordered pairs in table do not satisfy(equate) the equation.
<em>Checking B) y = -2x + 18</em>
<em>Putting (3, 12), (6, 18) and (9, 24) in y = -2x + 18</em>
- <em>For (3, 12) </em>⇒ y = -2x + 18 ⇒ 12 = -2(3) + 18 ⇒ 12 = 12 ⇒<em> L.H.S = R.HS</em>
- <em>For (6, 18)</em> ⇒ y = -2x + 18 ⇒ 18 = -2(6) + 18 ⇒ 18 = 6 ⇒ <em>L.H.S ≠ R.HS</em>
- <em>For (9, 24)</em> ⇒ y = -2x + 18 ⇒ 24 = -2(9) + 18 ⇒ 18 = 0 ⇒ <em>L.H.S ≠ R.HS</em>
So, y = -2x + 18 could have not produced all the values in the table, as (6, 18) does not equate the equation.
<em>Checking C) y = 2x + 6</em>
<em>Putting (3, 12), (6, 18) and (9, 24) in y = 2x + 6</em>
- <em>For (3, 12) </em>⇒ y = 2x + 6 ⇒ 12 = 2(3) + 6 ⇒ 12 = 12 ⇒<em> L.H.S = R.HS</em>
- <em>For (6, 18) </em>⇒ y = 2x + 6 ⇒ 18 = 2(6) + 6 ⇒ 18 = 18 ⇒<em> L.H.S = R.HS</em>
- <em>For (9, 24) </em>⇒ y = 2x + 6 ⇒ 24 = 2(9) + 6 ⇒ 24 = 24 ⇒<em> L.H.S = R.HS</em>
So, y = 2x + 6 could have produced the values of in the table as all the orders pairs in the table satisfy/equate the equation.
<em>Checking D) y = x + 9</em>
<em>Putting (3, 12), (6, 18) and (9, 24) in y = x + 9</em>
- <em>For (3, 12) </em>⇒ y = x + 9 ⇒ 12 = 3 + 9 ⇒ 12 = 12 ⇒<em> L.H.S = R.HS</em>
- <em>For (6, 18) </em>⇒ y = x + 9 ⇒ 18 = 6 + 9 ⇒ 18 = 15 ⇒ <em>L.H.S ≠ R.HS</em>
- <em>For (9, 24) </em>⇒ y = x + 9 ⇒ 24 = 9 + 9 ⇒ 24 = 18 ⇒<em> L.H.S ≠ R.HS</em>
So, y = x + 9 could have also not produced all the values in the table, as (6, 18) and (9, 24) do not satisfy/equate the equation.
So, from all the verification we conclude that:
<u>HENCE, ONLY </u><u>y = 2x + 6</u><u> COULD HAVE PRODUCED THE VALUES IN THE TABLE AS ALL THE ORDERED PAIRS OF THE TABLE SATISFY/EQUATE THE EQUATION.</u>
<em> </em><u><em>SOLVING QUESTIONS FROM 5th PAGE</em></u>
<em>What is the domain and range of the relation?</em>
{(-3, 7), (6, 2), (5, 1), (-9, -6)}
- Domain: Domain is the set of all the x-coordinates of the ordered pairs of the relation, meaning the all first elements of the ordered pairs in a relation include in the domain of the relation.
- Range: Range is the set of all the y-coordinate of the ordered pairs of the relation, meaning the all second elements of the ordered pairs in a relation include in the range of the relation.
As the given relation is {(-3, 7), (6, 2), (5, 1), (-9, -6)}
The <em>domain</em> is: {-3, 6, 5, -9}
<em>Note: generally, we write the numbers in ascending order for both the domain and range.</em>
The domain could also be written in order as: {-9, -3, 5, 6}
The <em>range</em> is: {7, 2, 1, -6}
The range could also be written in order as: {-6, 1, 2, 7}
Keywords: equation, point, ordered pair, domain, range
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