Question

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

Answer 1

Answer:

below

Step-by-step 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

Answer 2

Answer:

It does not form a linear equation.

Step-by-step explanation:

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

To work out the gradient, use $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

Using the top 2 rows, this gives $\frac{-1--3}{-2--6}$, or $\frac{2}{4}$, simplified to $\frac{1}{2}$. This means for every increase in x by 1, y increases by $\frac{1}{2}$.

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!