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

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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
What are the slope and the y-intercept of the linear function that is represented-example-1
User Everaldo Aguiar
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