Question

Find the x-intercept and y-intercept of the line .
-6x+5y=9

Answer 1

x-intercept:
`(-(3)/(2),0)`

y-intercept:
`(0,(9)/(5))`

Step-by-step explanation:

We have the following Line equation:

`-6x+5y=9`

x-intercpet:

If we want to find the x-intercept (the point where the line crosses with the x-axis), we have to set
`y=0`:

`-6x+5(0)=9`

`-6x=9`

`x=-(9)/(6)`

Simplifying:

`x=-(3)/(2)`

Hence, the x-intercept point is
`(-(3)/(2),0)`

y-intercept:

If we want to find the y-intercept (the point where the line crosses with the y-axis), we have to set
`x=0`:

`-6(0)+5y=9`

`5y=9`

`y=(9)/(5)`

Hence, the x-intercept point is
`(0,(9)/(5))`