Question

What is the function

X
- 1
0
1
2
3
у
-1
-0.5
0
0.5
1
The table represents
a linear function.
Write the function.
y=

Answer 1

Explanation:

x y Difference (d)

-1 -1 -

0 -0.5 -0.5 - (-1) = 0.5

1 0 0 - (-0.5) = 0.5

2 0.5 0.5 - 0 = 0.5

3 1 1 - 0.5 = 0.5

There is a common difference (d) = 0.5

Therefore, table represents a linear function.

Let the equation of the linear function is,

y = mx + b

Here, m = Slope and b = y-intercept

Since, slope of a line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` will be,

m =
`(y_2-y_1)/(x_2-x_1)`

Two points from the given table are (-1, -1) and (0, -0.5)

m =
`(-0.5-(-1))/(0-(-1))`

m = 0.5

Y-intercept of the line 'b' = -0.5 (Value of y at x = 0)

Therefore, equation of the line will be,

y = 0.5x - 0.5