Answer:
no
Step-by-step explanation:
Answer:
The slope is 3
The y-intercept is -2
The linear equation is y = 3x - 2
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is m =
∵ A line passes through points (2, 4) and (6, 16)
∴ x1 = 2 and y1 = 4
∴ x2 = 6 and y2 = 16
→ Substitute them in the rule of the slope above to find it
∵ m = 
= 
= 3
∴ m = 3
→ Substitute it in the form of the equation above
∴ y = 3x + b
→ To find b substitute x and y in the equation by the coordinates of
a point on the line
∵ Point (2, 4) is on the line
∴ x = 2 and y = 4
∵ 4 = 3(2) + b
∴ 4 = 6 + b
→ Subtract 6 from both sides to find b
∵ 4 - 6 = 6 - 6 + b
∴ -2 = b
→ Substitute its value on the equation above
∵ y = 3x + (-2)
∴ y = 3x - 2
→ Let us answer the questions
The slope is 3
The y-intercept is -2
The linear equation is y = 3x - 2
Part I - First synthetic division
You need to use synthetic division to come up with an expression for a and b:
(x + 2) is a factor, and the remainder is 7, so we can draw a synthetic division table...
coefficients = 1 for X^3; A for X^2; B for X^1; and 3
-2 | 1 A B 3
-2 -2(A-2) 4(A-2)-2B
1 (A-2) -2(A-2)+B 4(A-2)-2B + 3
Remainder = 7
<u>So...</u>
4(A-2)-2B + 3 = 7
4 * (A - 2) - 2B + 3 = 7
4A - 8 - 2B = 4
4A - 2B = 12
2A - B = 6
Proved
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Part II - Second Synthetic Division
We draw another synthetic division table, this time with (x - 1), so the number on the left hand side will be +1
1 | 1 A B 3
1 (A+1) A+B+1
1 (A+1) A+B+1 A+B+4
Remainder = 4
<u>So...</u>
A + B + 4 = 4
A + B = 0
<u>A = -B
</u>
-------------------------------------------------------------------------------------------------------------------
Part III - Solving for A and B with our two simultaneous equations
We know that<u> </u><u>A = -B</u><u /> and we also know that 2A - B = 6
Since we know that A is equal to -B We can substitute in A for -B, to get:
2A - B = 6
Therefore...
2A + A = 6
3A = 6
<u>A = 2</u>
Again, as we know that A = -B, and as we have found that A = 2, we can see:
A = -B
Therefore...
2 = -B
<u>B = -2
</u>
So our final answer is <u>A = 2, B = -2</u><u />
Hopefully this answer is more useful than the last one, and isn't so confusing!
Answer:
You would buy the DVD at Discount DVD.
Step-by-step explanation:
To decide where to buy the DVD, you have to determine the price at each store after the discount is applied.
-Discount DVD: $29.90*0.2=$5.98
$29.90-$5.98=$23.92
-Value Video: $28.60*0.15=$4.29
$28.60-$4.29=$24.31
According to this, you would buy the DVD at Discount DVD because it is where you will get the lower price.
