Question

Can the equation 2x + 5y = 10 be written as a linear function?

Answer 1

Answer: yes

Explanation:

A linear function is a function whose graph creates a straight line (where the x-variable is raised to the first power), one form of a linear function is slope-intercept form
`y=mx+b` where
`m` is the slope of the function and
`b` is the y-intercept (where the line crosses the y-axis).

To get the function
`2x+5y=10` in slope intercept form we must isolate the variable
`y`. We can do this by subtracting
`2x` from both sides:

`2x+5y=10`

`-2x`
`-2x`

`5y=10-2x`

Then we divide both sides by 5:

`5y=10-2x`

÷
`5` ÷
`5`

`y=(10)/(5)-(2x)/(5)`

And finally simplify fractions and rearrange the terms to match slope-intercept form.

`y=-(2)/(5) x+2`

This function is now in the linear slope-intercept form.