Answer: y = 0
Step-by-step explanation:
Each output has a value of 3 more than its input.
an = a(n-1) + 3
Missing number is 14 + 3 = 17.
If slope ofthe line is m=7, then the equation of the line is
![y=7x+b.](https://tex.z-dn.net/?f=y%3D7x%2Bb.)
Since line passes through the point (-4,-2), its coordinates satisfy the equation of the line:
![-2=7\cdot (-4)+b,\\ \\b=-2+28=26.](https://tex.z-dn.net/?f=-2%3D7%5Ccdot%20%28-4%29%2Bb%2C%5C%5C%20%5C%5Cb%3D-2%2B28%3D26.)
The equation of the line is
![y=7x+26.](https://tex.z-dn.net/?f=y%3D7x%2B26.)
Point (-5,k) lies on the line, then its coordinates satisfy the line equation:
![k=7\cdot (-5)+26=-35+26=-9.](https://tex.z-dn.net/?f=k%3D7%5Ccdot%20%28-5%29%2B26%3D-35%2B26%3D-9.)
Answer: k=-9.
Answer:
The equation of the line is:
![y = 28x](https://tex.z-dn.net/?f=y%20%3D%2028x)
Hence, option C is correct.
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
Given the table
Gallons Miles Driven
8 224
10 280
4 112
Finding the slope between any two points, let say (8, 224) and (10, 280)
![\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(8,\:224\right),\:\left(x_2,\:y_2\right)=\left(10,\:280\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%288%2C%5C%3A224%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%2810%2C%5C%3A280%5Cright%29)
![m=\frac{280-224}{10-8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B280-224%7D%7B10-8%7D)
![m=28](https://tex.z-dn.net/?f=m%3D28)
now substituting (8, 224) and m = 28 in the slope-intercept form of line equation
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
224 = 28(8) + b
224 = 224 + b
b = 0
Thus, the y-intercept b = 0
now substituting b = 0 and m = 28 in the slope-intercept form of line equation
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
![y = 28x+0](https://tex.z-dn.net/?f=y%20%3D%2028x%2B0)
![y = 28x](https://tex.z-dn.net/?f=y%20%3D%2028x)
Therefore, the equation of the line is:
![y = 28x](https://tex.z-dn.net/?f=y%20%3D%2028x)
Hence, option C is correct.