Question

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

Answer 1

Note: It seems you forgot to attach the table diagram. After a little research, I am able to find a table which is attached below.

Answer:

we conclude that:

• The slope = m = -2/5

• The y-intercept = b = -1/3

Explanation:

Finding the slope

Taking two points from the given table (check the attached diagram)

• (-3/4, -1/30)

• (-1/2, -2/15)

Finding the slope between (-3/4, -1/30) and (-1/2, -2/15)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`m=((-2)/(15)-(-1)/(30))/((-1)/(2)-(-3)/(4))`

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

Finding the y-intercept

We know that the slope-intercept form of the line equation is

`y=mx+b`

where m is the slope and b is the y-intercept.

Given

• 
  `m=-(2)/(5)`

• (-3/4, -1/30)

substitute to find the y-intercept (b)

`y=mx+b`

`\left((-1)/(30)\right)=-(2)/(5)\left((-3)/(4)\right)+b`

switch sides

`-(2)/(5)\left((-3)/(4)\right)+b=\left((-1)/(30)\right)`

`(3)/(10)+b=\left((-1)/(30)\right)`

`\mathrm{Subtract\:}(3)/(10)\mathrm{\:from\:both\:sides}`

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

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

Therefore, we conclude that:

• The slope = m = -2/5

• The y-intercept = b = -1/3