Solving Linear Functions

Linear functions are equations that describe a straight line on a graph. They can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Example Problem

Solve for $y$ in the equation $3x + 2y = 12$.

Step 1: Isolate the variable $y$

Subtract $3x$ from both sides:

$$2y = 12 - 3x$$

Step 2: Divide by the coefficient of $y$

Divide both sides by 2:

$$y = \frac{12 - 3x}{2}$$

Step 3: Simplify the expression

Separate the terms in the numerator:

$$y = \frac{12}{2} - \frac{3x}{2}$$

This simplifies to:

$$y = 6 - \frac{3}{2}x$$

Now we have the equation in slope-intercept form.

Key Questions

• What is the slope of the line represented by $2x + 5y = 10$?
• How do you convert the equation $y - 4 = 2(x + 1)$ into slope-intercept form?
• What is the y-intercept of the function $y = -3x + 7$?
• If $f(x) = 4x - 1$, what is $f(2)$?

Keywords

• Linear Function
• Slope
• Y-intercept
• Equation
• Slope-intercept Form