Respuesta :
The equations that represent the table are
- (a) [tex]y - 6 = -\frac 54(x + 2)[/tex]
- (d) [tex]y -1 = -\frac 54(x -2)[/tex]
- (e) [tex]y -3.5=-1.25x[/tex]
What are linear equations?
Linear equations are equations that have constant rates or slopes
From the complete question. the equation of the table is given as:
[tex]y - 6 = -\frac 54(x + 2)[/tex]
Add 5 to both sides of the equation
[tex]y - 6 + 5 = -\frac 54(x + 2) + 5[/tex]
[tex]y -1 = -\frac 54(x + 2) + 5[/tex]
Expand the bracket
[tex]y -1 = -\frac 54x -\frac 52 + 5[/tex]
Take LCM
[tex]y -1 = -\frac 54x +\frac {-5 + 10}2[/tex]
[tex]y -1 = -\frac 54x -\frac {5}2[/tex]
Factorize
[tex]y -1 = -\frac 54(x -2)[/tex]
Also, we have:
[tex]y - 6 = -\frac 54(x + 2)[/tex]
Open brackets
[tex]y -6 = -\frac 54x -\frac 52[/tex]
Express fractions as decimals
[tex]y -6 =-1.25x -2.5[/tex]
Add 2.5 to both sides
[tex]y -3.5=-1.25x[/tex]
Hence, the equations that represent the table are (a), (d) and (e)
Read more about linear functions at:
https://brainly.com/question/14323743