To find the slope and y-intercept of a linear function, we use a special way to write it called the slope-intercept form:

$y = mx + b$

Here’s what the letters mean:

• $m$ = slope (how steep the line is)
• $b$ = y-intercept (where the line crosses the y-axis)

Finding the Y-Intercept

To find the y-intercept, we need to set $x$ to 0 in the equation.

Here’s how to do it:

1. Substitute: Change $x$ to 0 in the equation.
2. Solve for $y$: The answer you get for $y$ when $x$ is 0 is the y-intercept.

For example, in the function $y = 2x + 3$, we replace $x$:

$y = 2(0) + 3 = 3$

So, the y-intercept is at the point $(0, 3)$.

Finding the Slope

The slope tells us how fast $y$ changes when $x$ changes. It is the number in front of $x$ in the slope-intercept form.

• If $m > 0$, the line goes up as you move to the right.
• If $m < 0$, the line goes down.
• If $m = 0$, the line is flat.

In our example $y = 2x + 3$, the slope $m$ is 2. This means when $x$ goes up by 1, $y$ goes up by 2.

Summary

• Y-Intercept: This can be found at the point $(0, b)$.
• Slope: The $m$ value shows how steep the line is.