Question

A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 3, negative 2, negative 1. The second column, y, has the entries 11.5, 17.25, 23, 28.75. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 3, negative 2, negative 1. The second column, y, has the entries, negative 5, negative 7.5, negative 10, negative 12.5.
The tables represent two linear functions. The equation represented by the first table is given below.

y = 5.75x + 34.5

What linear equation is represented by the second table?



What is the solution to the system of equations?

Answer 1

Second table: slope = (-7.5 − (−5))/(−3 − (−4)) = −2.5, intercept b from −5 = −2.5(−4)+b ⇒ b = −15.
So the second equation is y = −2.5x − 15 (or y = −5/2 x − 15).

Solve system: 5.75x + 34.5 = −2.5x − 15 ⇒ 8.25x = −49.5 ⇒ x = −6.
Then y = 0.

Solution: (−6, 0).