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.
[tex]\frac{9}{8}x +8y = 18\\[/tex]
[tex]\frac{9}{8}x +8 (0) = 18[/tex]
Now you need to clear x, later you will need to multiply 18 by 8 and divide by 9.
[tex](\frac{8}{9} )(\frac{9}{8})x = (\frac{8}{9} )18[/tex]
x = [tex]\frac{144}{9}[/tex]
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
.
[tex]\frac{9}{8} x +8y = 18[/tex]
first substract [tex]\frac{9}{8} x[/tex] in both sides of the equation:
[tex]\frac{9}{8} x-\frac{9}{8} x +8y = -\frac{9}{8} x + 18[/tex]
[tex]8y = -\frac{9}{8} x + 18[/tex]
Now divide by 8
[tex]y = -\frac{9}{8*8} x + \frac{18}{8}[/tex]
Then simplify
[tex]y = -\frac{9}{64} x + \frac{9}{4}[/tex]
Finally substitute x = 0, and you will find the value of y:
[tex]y = -\frac{9}{64} (0) + \frac{9}{4}[/tex]
[tex]y = \frac{9}{4}[/tex]
So the point is (0, [tex]\frac{9}{4}[/tex])
For the graph, substitute different values of x and solve for y in the equation [tex]y = -\frac{9}{64} x + \frac{9}{4}[/tex], you can see the graph in the attached file, also you will see the values in fracction and decimal points in the table.
