Answer:
The linear equation in the slope-intercept form will be:
![y\:=\:\frac{2}{3}x+64](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A%5Cfrac%7B2%7D%7B3%7Dx%2B64)
Step-by-step explanation:
From the line graph, taking two points
Finding the slope between (21, 78) and (27, 82)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(21,\:78\right),\:\left(x_2,\:y_2\right)=\left(27,\:82\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%2821%2C%5C%3A78%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%2827%2C%5C%3A82%5Cright%29)
![m=\frac{82-78}{27-21}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B82-78%7D%7B27-21%7D)
![m=\frac{2}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2%7D%7B3%7D)
We know that the slope-intercept of the line equation is
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
where m is the slope and b is the y-intercept
substituting (21, 78) and m = 2/3 in the slope-intercept of the line
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
![78=\frac{2}{3}\left(21\right)+b](https://tex.z-dn.net/?f=78%3D%5Cfrac%7B2%7D%7B3%7D%5Cleft%2821%5Cright%29%2Bb)
switch sides
![\frac{2}{3}\left(21\right)+b=78](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%5Cleft%2821%5Cright%29%2Bb%3D78)
![14+b=78](https://tex.z-dn.net/?f=14%2Bb%3D78)
![b=64](https://tex.z-dn.net/?f=b%3D64)
substituting b = 64 and m = 2/3 in the slope-intercept of the line
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
![y\:=\:\frac{2}{3}x+64](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A%5Cfrac%7B2%7D%7B3%7Dx%2B64)
Therefore, the linear equation in the slope-intercept form will be:
![y\:=\:\frac{2}{3}x+64](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A%5Cfrac%7B2%7D%7B3%7Dx%2B64)
You have 2 equations here, both already solved for y. Thus, you could eliminate y by equating the two functions. The resulting equation would depend only upon x. Do this. Solve for x. Then, substitute your value for x into either one of the given functions and calculate y. Present your answer in the form (x,y).
Answer:
Its the first answer!
Step-by-step explanation:
1/25, 1/5, 1 trust me on this one! sorry im a bit late!
Answer:
24/49
Step-by-step explanation:
The options to get 2 of different color is picking blue then red or red then blue.
Starting with picking blue then red.
The chance to pull blue first is 3/7. Then since the marble is replaced the chance to pull red next is 4/7.
The chance to get those in that specific order is the product of the two fractions. (3/7) * (4/7) = 12 / 49
The second option of getting red then blue will be the same as above but 4/7 then 3/7 with the same result of 12/49.
To finish, add the two probabilities together 12/49 + 12/49 = 24/49.