Question

The table represents a linear function. What is the slope of the function?

Answer 1

Answer: 3

Explanation:

In theory we know that the equation of a linear function is expressed as

Eq.(1): y = m*x + c,

where m is the slope and c is a constant.

From the table we know the values of x and y, so we can use any of those, but in this case lets use the first and third rows of the table and substituting in Eq.(1) we obtain a 2-equation system as follow:

Point (-2,-2) gives: -2 = (-2)*m + c Eq.(2)

Point (0,4) gives: 4 = (0)*m + c Eq.(3)

Now rearranging Eq.(2) we get: -2 = -2*m + c <=> -2 - c = -2m Eq.(4)

Then rearranging Eq.(3) we get: 4 = 0 + c <=> c = 4

Plugging the value of c in Eq.(4) we get:

-2 = -2m + 4 <=> -2 - 4 = - 2m <=> -6 = -2m <=> m = 3

So finally and from Eq.(1) we obtain

y = 3x + c

Answer 2

Answer: 3

Explanation:

We know that the slope of a function is given by :-

`\text{slope}=\frac{\text{Change in y values}}{\text{Change in x values}}`

By considering the given table, from x= 0 to x= 1 , the slope of the function will be :-

`\text{slope}=(7-4)/(1-0)\\\\\Rightarrow\ \text{slope}=3`

Therefore , the slope of the function= 3