Question

1. Explain, without graphing, how you can determine whether the table below represents a

linear equation
X
y
-6-3
-2-1
0
1
1
2
4
6

Answer 1

It does not form a linear equation.

Explanation:

For this question, you should check that they all have the same gradient.

To work out the gradient, use
`(y_(2)-y_(1))/(x_(2)-x_(1))`.

Using the top 2 rows, this gives
`(-1--3)/(-2--6)`, or
`(2)/(4)`, simplified to
`(1)/(2)`. This means for every increase in x by 1, y increases by
`(1)/(2)`.

Between the first 2 rows, x increases by 4 and y by 2 (half of 4), so it is true.

Between the second and third rows, x increases by 2 and y by 2 (which isn't half of 2). This is false, meaning this does not form a linear equation.

**This question involves solving linear equations using gradients, which you may want to revise. I'm always happy to help!

Answer 2

below

Explanation:

you can find the distance between the y values for each x value and if it comes out to be an even increase/decrease you know it is linear