Answer:
x-intercept (16, 0), y-intercept (0, 9/4)
Step-by-step explanation:
In order to find the x-intercept from your equation, you can substitute y = 0, then solve for x.
![\frac{9}{8}x +8y = 18\\](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B8%7Dx%20%2B8y%20%3D%2018%5C%5C)
![\frac{9}{8}x +8 (0) = 18](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B8%7Dx%20%2B8%20%280%29%20%3D%2018)
Now you need to clear x, later you will need to multiply 18 by 8 and divide by 9.
![(\frac{8}{9} )(\frac{9}{8})x = (\frac{8}{9} )18](https://tex.z-dn.net/?f=%28%5Cfrac%7B8%7D%7B9%7D%20%29%28%5Cfrac%7B9%7D%7B8%7D%29x%20%3D%20%28%5Cfrac%7B8%7D%7B9%7D%20%2918)
x = ![\frac{144}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B144%7D%7B9%7D)
x = 16
The point is (16, 0)
Now, for finding the y-intercept
Since you have the equation, you need to change it to slope intercept form, remember the general equation is Y = mX + b
.
![\frac{9}{8} x +8y = 18](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B8%7D%20x%20%2B8y%20%3D%2018)
first substract
in both sides of the equation:
![\frac{9}{8} x-\frac{9}{8} x +8y = -\frac{9}{8} x + 18](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B8%7D%20x-%5Cfrac%7B9%7D%7B8%7D%20x%20%2B8y%20%3D%20-%5Cfrac%7B9%7D%7B8%7D%20x%20%2B%2018)
![8y = -\frac{9}{8} x + 18](https://tex.z-dn.net/?f=8y%20%3D%20-%5Cfrac%7B9%7D%7B8%7D%20x%20%2B%2018)
Now divide by 8
![y = -\frac{9}{8*8} x + \frac{18}{8}](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B9%7D%7B8%2A8%7D%20x%20%2B%20%5Cfrac%7B18%7D%7B8%7D)
Then simplify
![y = -\frac{9}{64} x + \frac{9}{4}](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B9%7D%7B64%7D%20x%20%2B%20%5Cfrac%7B9%7D%7B4%7D)
Finally substitute x = 0, and you will find the value of y:
![y = -\frac{9}{64} (0) + \frac{9}{4}](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B9%7D%7B64%7D%20%280%29%20%2B%20%5Cfrac%7B9%7D%7B4%7D)
![y = \frac{9}{4}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B9%7D%7B4%7D)
So the point is (0,
)
For the graph, substitute different values of x and solve for y in the equation
, you can see the graph in the attached file, also you will see the values in fracction and decimal points in the table.