Answer:
Equation in slope-intercept form that goes through (12, 4) and (20,8) is: ![y = \frac{1}{2}x-2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx-2)
Step-by-step explanation:
Given two points are:
![(x_1,y_1) = (12,4)\\(x_2,y_2) = (20,8)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%2812%2C4%29%5C%5C%28x_2%2Cy_2%29%20%3D%20%2820%2C8%29)
Slope intercept form of line is given as:
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
Here m is the slope of the line and b is the y-intercept.
Slope of a line is calculated by the formula:
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Putting the values
![m = \frac{8-4}{20-12}\\m = \frac{4}{8}\\m=\frac{1}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B8-4%7D%7B20-12%7D%5C%5Cm%20%3D%20%5Cfrac%7B4%7D%7B8%7D%5C%5Cm%3D%5Cfrac%7B1%7D%7B2%7D)
Putting the value of slope in slope-intercept form we get
![y = \frac{1}{2}x+b](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%2Bb)
To find the value of b, any one point will be put in the equation
Putting the first point (12,4) in the equation
![4 = \frac{1}{2}(12) + b\\4 = 6+b\\b = 4-6\\b = -2](https://tex.z-dn.net/?f=4%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2812%29%20%2B%20b%5C%5C4%20%3D%206%2Bb%5C%5Cb%20%3D%204-6%5C%5Cb%20%3D%20-2)
Putting the value of b
![y = \frac{1}{2}x-2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx-2)
Hence,
Equation in slope-intercept form that goes through (12, 4) and (20,8) is: ![y = \frac{1}{2}x-2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx-2)
Answer:
area = (1/2)|Ax(By-Cy) +Bx(Cy-Ay) +Cx(Ay-By)|
= (1/2)|2(3-6) +3(6-1) +1(1-3)| = (1/2)|-6 +15 -2|
area = 7/2
learn at brainly.com/question/17119045
Area of the trapezoid:
![\frac{12.8 + 4.2}{2} (4.9) = 41.65 cm^2](https://tex.z-dn.net/?f=%20%5Cfrac%7B12.8%20%2B%204.2%7D%7B2%7D%20%284.9%29%20%3D%2041.65%20cm%5E2)
Area of the rectangle:
4.2 x 3.1 = 13.02 cm^2
Area of each quarter circle:
![\frac{ \pi (3.1)^{2} }{4} = 7.54 cm^2](https://tex.z-dn.net/?f=%20%20%5Cfrac%7B%20%5Cpi%20%20%283.1%29%5E%7B2%7D%20%7D%7B4%7D%20%3D%207.54%20cm%5E2)
We have two quarter circles:
7.54 + 7.54 = 15.08
41.65 + 13.02 + 15.08 = 69.75 cm^2
Sorry i really need points