Question

Find the x-intercept and the y-intercept of the graph of the equation 9/8x + 8y = 18. Then graph the equation.

Answer 1

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.

$\frac{9}{8}x +8y = 18$

$\frac{9}{8}x +8 (0) = 18$

Now you need to clear x, later you will need to multiply 18 by 8 and divide by 9.

$(\frac{8}{9} )(\frac{9}{8})x = (\frac{8}{9} )18$

x = $\frac{144}{9}$

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 .

$\frac{9}{8} x +8y = 18$

first substract $\frac{9}{8} x$ in both sides of the equation:

$\frac{9}{8} x-\frac{9}{8} x +8y = -\frac{9}{8} x + 18$

$8y = -\frac{9}{8} x + 18$

Now divide by 8

$y = -\frac{9}{8*8} x + \frac{18}{8}$

Then simplify

$y = -\frac{9}{64} x + \frac{9}{4}$

Finally substitute x = 0, and you will find the value of y:

$y = -\frac{9}{64} (0) + \frac{9}{4}$

$y = \frac{9}{4}$

So the point is (0, $\frac{9}{4}$)

For the graph, substitute different values of x and solve for y in the equation $y = -\frac{9}{64} x + \frac{9}{4}$, you can see the graph in the attached file, also you will see the values in fracction and decimal points in the table.

Download xlsx