Understanding Slope and Intercept of a Linear Function

Knowing how to find the slope and intercept of a linear function is an important skill in Year 8 Math. Let's make it simple!

What is a Linear Function?

A linear function can be written as an equation like this:

$$y = mx + b$$

In this equation,

• $y$ is the result we get.
• $x$ is the number we put in.
• $m$ is the slope, which tells us how steep the line is.
• $b$ is the y-intercept, where the line crosses the y-axis.

Finding the Slope ($m$)

The slope shows how steep the line is and which way it goes. We can figure this out using the formula:

$$m = \frac{\text{change in } y}{\text{change in } x}$$

Let’s look at an example. If a line goes through the points (1, 2) and (3, 6):

• The change in $y$: $6 - 2 = 4$
• The change in $x$: $3 - 1 = 2$

So, the slope $m$ is:

$$m = \frac{4}{2} = 2$$

This means the line is pretty steep!

Finding the Y-Intercept ($b$)

The y-intercept is where the line touches the y-axis. This happens when $x = 0$.

You can find $b$ easily from the equation. For example, in the equation $y = 2x + 1$, we can see that $b = 1$.

This tells us that the line crosses the y-axis at the point (0, 1).

Summary

To find the slope and intercept:

1. Look for the equation in the form $y = mx + b$.
2. Find $m$ by calculating the rise over run between two points.
3. Get $b$ by putting $x = 0$ in the equation or just reading it from there.

With these steps, you’re on your way to understanding linear functions!