Slope intercept form is y = mx + b.
Y = coordinate y.
M = Slope
X = coordinate x.
B = y-intercept.
Slope formula: (y2-y1) / (x2-x1)
Plug in: (-1 - 7) / (4 - 2) = -4.
We can just insert the pair (2,7) as our x and y to solve b.
7 = -4(2) + b.
Solve for b.
7 = -8 + b.
-b = -8 -7
-b = -15
b = 15.
Original equation:
y = mx + b
y = -4x + 15
Answer:
A) x=9/2 B) x=-1/5, 1/2
Step-by-step explanation:
3x-9=27/1-5x
3x-9=27-5x
3x-(-5x)-9=27
3x+5x-9=27
8x-9=27
8x=27+9
8x=36
x=36/8
simplify
x=9/2
Answer: x=9/2
-----------------------------
10x-1/x=3
(10x^2-1)/x=3
10x^2-1=3*x
10x^2-1=3x
10x^2-3x-1=0
factor out the trinomial,
find two numbers that when they multiply,
you get the third term, which is -1 in this case.
When you add those 2 numbers, you get the second term,
which is -3 in this case.
(5x+1)(2x-1)=0
apply the zero property from here,
set 5x+1=0 and 2x-1=0 and solve for x.
5x=0-1=-1, x=-1/5,
2x=0+1=1, 2x=1, x=1/2.
So x=-1/5, 1/2.
You are told to choose the choices equal to T(8). T(8) means that you need to find the possible ways to write the y-value when n = 8, since 8 is being substituted in for "n."
1) First, plug in n = 8 into the equation you're given, <span>T(n) = 4n - 5:
T(8) = 4(8) - 5
T(8) = 32 - 5
T(8) = 27
That is answer choice C, making choice C correct. You can eliminate choice B, since 27 </span>≠ 37.
2) Check answer choice A. Is T(5) + T(3) = 27? T(5) means you need to plug in 5 for n. T(3) means you need to plug in 3 for n.
T(5) + T(3)
= [4(5) - 5] + [4(3) - 5]
= [20-5] + [12-5]
= 15 + 7
= 22
Since 22 ≠ 27, you can eliminate choice A.
3) Check answer choice D. Is T(7) + 4 = 27? T(7) means you need to plug in 7 for n.
T(7) + 4
= [<span>4(7) - 5] + 4
</span>= [28 - 5] + 4
= 23 + 4
= 27
Since 27 = 27, answer choice D is also correct!
--------
Answer: Choice C (27) and Choice D (T(7) + 4)
