Question

Describe the pattern in the table using words, an equation, and a graph. Extend the pattern for x=5, 6 and 7.

Answer 1

Explanation:

x y Difference
`(y_2-y_1)`

1 15 -

2 25 25 - 15 = 10

3 35 35 - 25 = 10

4 45 45 - 35 = 10

There is a common difference of 10 in each successive term of y.

Therefore, table represents a linear function.

Let the equation of the linear function is,

y = mx + b

Here 'm' = slope of the line

b = y-intercept

Since, two points (1, 15) and (2, 25) lie on the graph of the function,

Slope of the line =
`(y_2-y_1)/(x_2-x_1)`

m =
`(25-15)/(2-1)`

m = 10

Equation of the line will be,

y = 10x + b

For the value of 'b' (y-intercept),

Since, (1, 15) lies on the graph of the linear function,

15 = 10(1) + b

b = 15 - 10

b = 5

Equation of the line on the graph will be,

y = 10x + 5

Now we can determine the output value of the function with the input values, x = 5, 6 and 7

`y_1` = 10(5) + 5 = 55

`y_2` = 10(6) + 5 = 65

`y_3` = 10(7) + 5 = 75