Question

What is the function

Answer 1

Answer:

Step-by-step 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 = $\frac{y_2-y_1}{x_2-x_1}$

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

m = $\frac{-0.5-(-1)}{0-(-1)}$

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