let's bear in mind that Y is a bisecting point, so it's really cutting XZ into two equal halves.
![\bf \underset{\textit{\Large 18x-6}}{\boxed{X}\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}} Y\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}}\boxed{Z}} \\\\\\ 12x+12x = 18x-6\implies 24x=18x-6 \\\\\\ 6x=-6\implies x=\cfrac{-6}{6}\implies x=-1](https://tex.z-dn.net/?f=%5Cbf%20%5Cunderset%7B%5Ctextit%7B%5CLarge%2018x-6%7D%7D%7B%5Cboxed%7BX%7D%5Cstackrel%7B12x%7D%7B%5Crule%5B0.35em%5D%7B14em%7D%7B0.25pt%7D%7D%20Y%5Cstackrel%7B12x%7D%7B%5Crule%5B0.35em%5D%7B14em%7D%7B0.25pt%7D%7D%5Cboxed%7BZ%7D%7D%20%5C%5C%5C%5C%5C%5C%2012x%2B12x%20%3D%2018x-6%5Cimplies%2024x%3D18x-6%20%5C%5C%5C%5C%5C%5C%206x%3D-6%5Cimplies%20x%3D%5Ccfrac%7B-6%7D%7B6%7D%5Cimplies%20x%3D-1)
The basic structure of a linear function is y=mx+b (or +c, depending on your schools curriculum)
We need to find the slope (m), and the y-intercept (b/c)
To find the slope you can pick two random points, say (2,2) and (0,1)
The formula for the slope is this: m= y1-y2 / x1-x2
So if we substitute the points in, we get 2-1 / 2-0 = 1/2
Knowing the slope, it can be substituted into to the equation: y=1/2x + b
Then, if you notice the second point- (0,1), it’s the y-intercept. The y coordinate there is 1.
To check if this is correct, a random coordinate set can be picked and substituted in to find b.
y= 1/2x + b
2 = 1/2 *2 + b
2 = 1 + b
2-1=b
1=b
Therefore, the final linear function is y = 1/2 x + 1
Hello there!
The correct answer is option C
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Graph using the slope and y- intercept
Slope: -3
Y-intercept: 1
Good luck with your studies!
15.545
Step-by-step explanation: