Graphing linear functions is an important skill in Algebra that every student needs to learn. Here are the key things you should know:

1. What is a Linear Function?

A linear function is a way to show a relationship between two things using the equation $y = mx + b$. In this equation:

• $m$ is the slope, which tells us how steep the line is.
• $b$ is the y-intercept. This is where the line crosses the y-axis (the vertical line on the graph).

2. What is Slope?

The slope $m$ shows how much $y$ changes when $x$ changes. We can find the slope with this formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Here, it measures the change in $y$ for each change in $x$.

• If the slope is positive (like $m=1$), the line goes up.
• If the slope is negative (like $m=-1$), the line goes down.

3. Y-Intercept

The y-intercept $b$ is very important for graphing linear functions. Every linear equation has one y-intercept.

For example, in the equation $y = 2x + 3$, the line crosses the y-axis at the point $(0, 3)$.

4. How to Plot Points

To draw the graph of a linear function, follow these steps:

• Start at the y-intercept.
• Use the slope to find another point. For example, from the y-intercept, if you go up 2 units and 1 unit to the right, you'll find another point on the line.

5. What Do Linear Graphs Look Like?

• Straight Line: When you graph linear functions, they create straight lines.
• Continuity: The lines can go on forever in both directions.
• Constant Rate of Change: The slope stays the same, showing a steady relationship.

Knowing these features helps students understand more complicated graphs and how they can be used in real life.