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:
 $m = \frac{b2-b1}{a2-a1}$
 Substituting values:
 $m = \frac{-7-(-10)}{1-0}$
 Rewriting:
 $m = \frac{-7+10}{1}$
 $m = 3$
 Thus, the linear equation is:
 $b = 3*a-10$
 Rewriting:
 $3*a-b=10$
 Answer:
 The equation is:
 C.) 3a-b=10