Step 1: Find the slope:
This gives you 
, but we need to find b.
To find b, substitute in one (x,y) pair and it doesn't matter which one. I'll go with (4,-2):
![\begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-2%26%3D-%5Cdfrac%7B3%7D%7B2%7D%284%29%2Bb%5C%5C%5B0.5em%5D-2%26%3D-6%2Bb%5C%5C%5B0.5em%5D4%26%3Db%5Cend%7Baligned%7D)
Now take that b-value and plug in into the slope-intercept form:
It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.
Answer:
The solutions are:
Step-by-step explanation:
We have the following quadratic equation
We can rewrite the equation as follows
Now we use the quadratic formula to solve the equation
For an equation of the form 
the quadratic formula is:
In this case:
Then:
Given:
A rectangular piece of cloth (dimensions):
L = length of the rectangle
W = width of the rectangle
The area of the rectangle is:
A = L x W
If the cloth is cut along the diagonal, the area of one sail will be half the area of the rectangle:
A (one sail) = 1/2 (L x W) <span />
Answer:
4512 handshakes
Step-by-step explanation:
We are told in the question, that there are
96 people in the room = 48 couples
Assuming that no husband or wife shakes each others hand but everyone else shakes hands exactly once
This means
48 couples will shake 94 people because they are excluded
This is calculated as
48 × 94 = 4512 handshakes
Slope = (-2 - 10)/(12 + 6) = -12/18 = -2/3
y = mx + b
10 = -2/3(-6) + b
10 = 4 + b
b =6
equation
y = -2/3x + 6
<span>x-intercept when y = 0
</span>-2/3x + 6 = 0
-2/3x = -6
x = 6 (3/2)
x = 9
answer is <span>d.9</span>
