Question

Which equation satisfies all three pairs of a and b values listed in the table?

a b
0 -10
1 -7
2 -4
Is the equation?
A.) a-3b=10
B.) 3a+b=10
C.) 3a-b=10
D.) a+3b=10

Answer 1

We observe that the relationship between the variables is linear.
Therefore, we look for an equation of the form:

`b = m * a + b '`
Where,
m: slope of the line
b ': intersection with the y axis
a: independent variable
b: dependent variable
The value of b 'occurs when a = 0.
We have then:

`b '= -10`
(See table)
Then, the value of the slope is found using the following formula:

`m = (b2-b1)/(a2-a1)`
Substituting values:

`m = (-7-(-10))/(1-0)`
Rewriting:

`m = (-7+10)/(1)`

`m = 3`
Thus, the linear equation is:

`b = 3*a-10`
Rewriting:

`3*a-b=10`
Answer:
The equation is:
C.) 3a-b=10