Question

solving a system represented in a table
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?

first table (x, y):
-4, 11.5
-3, 17.25
-2, 23
-1, 28.75

second table (x, y):
-4, -5
-3, -7.5
-2, -10
-1, -12.5

Explanation:

Step1: Find slope of second table

Use two points \((-4, -5)\) and \((-3, -7.5)\). Slope \(m=\frac{-7.5 - (-5)}{-3 - (-4)}=\frac{-2.5}{1}=-2.5\) (or \(-\frac{5}{2}\)).

Step2: Find y - intercept (b)

Use point \((-4, -5)\) and \(y = mx + b\). Substitute: \(-5=-2.5(-4)+b\) → \(-5 = 10 + b\) → \(b=-15\). So equation is \(y=-2.5x - 15\) (or \(y = -\frac{5}{2}x-15\)).

Step3: Solve system \(y = 5.75x+34.5\) and \(y=-2.5x - 15\)

Set equal: \(5.75x + 34.5=-2.5x-15\). Add \(2.5x\): \(8.25x + 34.5=-15\). Subtract 34.5: \(8.25x=-49.5\). Divide by 8.25: \(x=\frac{-49.5}{8.25}=-6\). Substitute \(x = -6\) into \(y=-2.5x - 15\): \(y=-2.5(-6)-15 = 15 - 15 = 0\).

Answer:

Linear equation for second table: \(y=-2.5x - 15\) (or \(y = -\frac{5}{2}x-15\))
Solution to system: \((-6, 0)\)