Question

The table `((x:, 3, 4, n, 8),(y:, 5,7,11,15))` describes a linear function. How do you express the function in slope intercept form and find the value of `n` ?

Answer 1

`y=2x-1" "` and `" "n = 6`

Explanation:

Given:

`((x:, 3, 4, n, 8),(y:, 5,7,11,15))`

We want to find the linear equation and solve for `n`.

The equation may be written in the form:

`y = mx+c`

for some constants `m` and `c` to be determined.

This must be satisfied by the table entries we are given.

So:

`{ (color(blue)(5) = color(blue)(3)m+c), (color(blue)(7) = color(blue)(4)m+c), (color(blue)(11) = color(blue)(n)m+c), (color(blue)(15)=color(blue)(8)m+c) :}`

Subtracting the first of these equations from the second, we find:

`2 = m`

Then substituting `m=2` in the first equation, we have:

`5=3*2+c = 6+c`

Hence:

`c = -1`

Check the fourth equation:

`2*color(blue)(8)-1 = 16-1=color(blue)(15)" "` as required.

Then the third equation becomes:

`2color(blue)(n)-1 = color(blue)(11)`

Add `1` to both sides to get:

`2n=12`

Divide both sides by `2` to find:

`n=6`