Question

What are the slope and the y-intercept of the linear function that is represented by the table?

-1
у
3
2
1
2
0
0
اني انا
3
1
2

Answer 1

`m = -(2)/(5)` ---- slope

`y = -(1)/(3)` --- y intercept

Explanation:

Given

The attached table

Required

Calculate the slope and y intercept

First, we need to calculate the slope

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

From the table, the following relationships exist:

`(x_1,y_1) = (-(3)/(4),-(1)/(30))`

`(x_2,y_2) = ((1)/(4),-(13)/(30))`

So, the expression for calculating slope becomes:

`m = [-(13)/(30) - (-(1)/(30))] / [(1)/(4) - (-(3)/(4))]`

`m = [-(13)/(30) +(1)/(30)] / [(1)/(4) +(3)/(4)]`

Take LCM

`m = [(-13+1)/(30)] / [(1+3)/(4)]`

`m = [(-12)/(30)] / [(4)/(4)]`

`m = [(-12)/(30)] / 1`

`m = (-12)/(30)`

`m = (-2)/(5)`

`m = -(2)/(5)`

To calculate the y intercept:

x must be 0. i.e.

`x = 0`

So, we have:

`(x_1,y_1) = (-(3)/(4),-(1)/(30))`

`(x_2,y_2) = (0,y)`

`m = -(2)/(5)`

Substitute these values in:

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

`-(2)/(5) = [y - (-(1)/(30))] / [0- (-(3)/(4))]`

`-(2)/(5) = [y +(1)/(30)] / [0+(3)/(4)]`

`-(2)/(5) = [y +(1)/(30)] / [(3)/(4)]`

Multiply through by 3/4

`-(2)/(5)*(3)/(4) = y +(1)/(30)`

`-(6)/(20) = y +(1)/(30)`

`-(3)/(10) = y +(1)/(30)`

Collect Like Terms

`y = -(3)/(10)-(1)/(30)`

`y = (-9-1)/(30)`

`y = (-10)/(30)`

`y = (-1)/(3)`

`y = -(1)/(3)`