Question

How do you find the x and y intercepts of `5y=7.5-2.5x`?

Answer 1

`y_("intercept")=3/2`

`x_("intercept")=3`

Explanation:

Lets get rid of the decimals. Multiply both sides by 2

`2(5y)=2(7.5-2.5x)`

`10y=15-5x`

Divide both sides by 10

`y=15/10-5/10x`

`y=3/2-1/2x`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
y intercept is at `x=0` so by substitution

`y_("intercept")" "=" "3/2-1/2(0)" "=" "3/2`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x intercept is at `y=0` so by substitution

`0=3/2-1/2(x_("intercept"))`

`=> +1/2(x_("intercept"))=3/2`

`x_("intercept")=3`

Answer 2

x intercept is 3
y intercept is 1.5

Explanation:

To find x intercept we should substitute `y` by zero
To find y intercept we should substitute `x` by zero

x intercept for the given equation:
`5(0)=7.5-2.5x`
`rArr 0= 7.5-2.5x`
`rArr 0=7.5-2.5x`
`rArr-7.5=-2.5x`
`rArrx=(-7.5)/-2.5`
`rArrx=3`

y intercept of the given equation:
`5y=7.5-2.5(0)`
`rArr5y=7.5-0`
`rArr5y=7.5`
`rArry=7.5/5`
`rArry=1.5`

Therefore, x intercept is 3 and y intercept is 1.5