Question

Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)?

f(x) = x + 4
f(x) = x + 6
f(x) = x – 10
f(x) = x – 12

Answer 1

Option 1st is correct

`f(x) = x+4`

Explanation:

Given the point-slope equation:

`y-8 = 1(x-4)`

Apply the distributive property:
`a\cdot (b+c) = a\cdot b+ a\cdot c`

⇒
`y-8 = x-4`

Add 8 to both sides we have;

`y-8+8 = x-4+8`

Simplify:

`y = x+4`

Use notation: y = f(x)

then;

`f(x) = x+4`

Therefore, the linear function represents the line given by the point-slope equation y – 8 = (x – 4) is,
`f(x) = x+4`

Answer 2

y -8 = x - 4

y = x -4 + 8

y = x + 4

where y = f(x) ( y is a function of x meaning that y value is determined with the help of the value of x)

f(x) = x +4