Question

Fill in the table so it represents a linear function.

Answer 1

Answer:

-1, 2, 5, 8, 11

Step-by-step explanation:

There is an easy and fast way to solve this. A linear function means that the steps on y and x are constant.

On the x axis you are walking 5 steps each column, so you start from 5, plus 5 steps is 10, plus 5 steps is 15, plus 5 steps is 20, plus 5 steps is 25.

Now you have to do the same for the y axis, but you have to use your brain.

You start from -1, and you have to reach 11, using the same number of steps for each column, just like before the necessarily with the same number.

You start from -1, plus 3 steps is 2, plus 3 steps is 5, plus 3 steps is 8, plus 3 steps is 11. Done.

You can use maths also, but it will take time.

You need to find that function. A linear function can be written as:

$y = mx + q$

You have two points of the line, (5, -1) and (25, 11), but you need to find the y coordinate of other three points.

Let's find the line by substituting those points in the general function of the line:

$- 1 = 5m + q \\ 11 = 25m + q$

This is a system of two equations with two variables, m and q. You can solve it. From the first equation you have that:

$q = - 1 - 5m$

Put this in the second equation to know the value of m:

$11 = 25m + ( - 1 - 5m)$

$11 = 25m - 1 - 5m \\ 20m = 12 \\ m = \frac{12}{20} = \frac{3}{5}$

Now you can use this in the first equation to know the value of q:

$q = - 1 - 5( \frac{3}{5} ) \\ q = - 1 - 3 \\ q = - 4$

So your line is:

$y = \frac{3}{5} x - 4$

If you want to know the y coordinates that you are missing, you just need to put the corresponding x coordinate in this function and you will find the same results as before.