Answer:
<u>3 5 = 16</u>
<u> 3 = 3 16</u>
<u> 6 = 16</u>
<u> 6 = -4</u>
<u> x = -4/6</u>
each line has the number of boxes to be filled
Answer:
A) y will increase by 4 unit.
B) y will decrease by 20 units
Step-by-step explanation:
Given equation that shows relation between x and y.
![y=4x-3](https://tex.z-dn.net/?f=y%3D4x-3)
A) If x is increased by 4 units
New value of y = ![4(x+1)-3](https://tex.z-dn.net/?f=4%28x%2B1%29-3)
![=4x+4-3](https://tex.z-dn.net/?f=%3D4x%2B4-3)
![=4x+1](https://tex.z-dn.net/?f=%3D4x%2B1)
So, change in y = new value of y- original value of y
![=4x+1-(4x-3)](https://tex.z-dn.net/?f=%3D4x%2B1-%284x-3%29)
![=4x+1-4x+3](https://tex.z-dn.net/?f=%3D4x%2B1-4x%2B3)
![=4](https://tex.z-dn.net/?f=%3D4)
Thus, the value of y will be increased by 4 units.
B) If x is decreased by 5 units
New value of y = ![4(x-5)-3](https://tex.z-dn.net/?f=4%28x-5%29-3)
![=4x-20-3](https://tex.z-dn.net/?f=%3D4x-20-3)
![=4x-23](https://tex.z-dn.net/?f=%3D4x-23)
So, change in y = new value of y- original value of y
![=4x+1-(4x-3)](https://tex.z-dn.net/?f=%3D4x%2B1-%284x-3%29)
![=4x-23-(4x-3)](https://tex.z-dn.net/?f=%3D4x-23-%284x-3%29)
![=4x-23-4x+3](https://tex.z-dn.net/?f=%3D4x-23-4x%2B3)
= -20
Thus, the value of y will be decreased by 20 units.
Answer: (-6, 5)
<u>Step-by-step explanation:</u>
Use the Midpoint Formula: ![\dfrac{(x_k, y_k)+(x_L,y_L)}{2}=(x_m, y_m)](https://tex.z-dn.net/?f=%5Cdfrac%7B%28x_k%2C%20y_k%29%2B%28x_L%2Cy_L%29%7D%7B2%7D%3D%28x_m%2C%20y_m%29)
Separate the x's and y's and solve them individually:
![\dfrac{x_k+x_L}{2}=x_m\qquad \qquad \qquad \qquad\dfrac{y_k+y_L}{2}=y_m\\\\\\\dfrac{x_k+8}{2}=1\qquad \qquad \qquad \qquad \qquad \dfrac{y_k-7}{2}=-1\\\\\\x_k+8=2\qquad \qquad \qquad \qquad \qquad y_k-7=-2\\\\\\x_k\quad =-6 \qquad \qquad \qquad \qquad \qquad y_k\qquad =5](https://tex.z-dn.net/?f=%5Cdfrac%7Bx_k%2Bx_L%7D%7B2%7D%3Dx_m%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%5Cdfrac%7By_k%2By_L%7D%7B2%7D%3Dy_m%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bx_k%2B8%7D%7B2%7D%3D1%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cdfrac%7By_k-7%7D%7B2%7D%3D-1%5C%5C%5C%5C%5C%5Cx_k%2B8%3D2%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20y_k-7%3D-2%5C%5C%5C%5C%5C%5Cx_k%5Cquad%20%3D-6%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20y_k%5Cqquad%20%3D5)
So, the k-coordinate is (-6, 5)