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
We observe that the relationship between the variables is linear. Therefore, we look for an equation of the form: [tex]b = m * a + b '
[/tex] 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: [tex]b '= -10
[/tex] (See table) Then, the value of the slope is found using the following formula: [tex]m = \frac{b2-b1}{a2-a1} [/tex] Substituting values: [tex]m = \frac{-7-(-10)}{1-0} [/tex] Rewriting: [tex]m = \frac{-7+10}{1} [/tex] [tex]m = 3 [/tex] Thus, the linear equation is: [tex]b = 3*a-10 [/tex] Rewriting: [tex]3*a-b=10 [/tex] Answer: The equation is: C.) 3a-b=10
