Question

solve and write the equation in function form f(x).

1. - 3x + y = 12
2. x - 3y = 12

use a table to graph a function.

1. y = 3x - 1
2. f(x) = 4x - 2

use the x and the y intercepts to graph the function.

1. x + 5y = 8
2. y = - 3/2x + 3

Explanation:

Problem 15:

Step1: Isolate y

Start with \(-3x + y = 12\). Add \(3x\) to both sides: \(y = 3x + 12\).

Step2: Rewrite as f(x)

Replace \(y\) with \(f(x)\): \(f(x) = 3x + 12\).

Step1: Isolate y

Start with \(x - 3y = 12\). Subtract \(x\): \(-3y = -x + 12\). Divide by \(-3\): \(y = \frac{1}{3}x - 4\).

Step2: Rewrite as f(x)

Replace \(y\) with \(f(x)\): \(f(x) = \frac{1}{3}x - 4\).

Step1: Create a table

Choose \(x\)-values (e.g., \(x = -1, 0, 1\)):

• \(x = -1\): \(y = 3(-1) - 1 = -4\)
• \(x = 0\): \(y = 3(0) - 1 = -1\)
• \(x = 1\): \(y = 3(1) - 1 = 2\)

Step2: Plot points

Plot \((-1, -4)\), \((0, -1)\), \((1, 2)\) on the left graph and draw a line through them.

Answer:

\(f(x) = 3x + 12\)

Problem 16: