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# Finding the Slope from a Linear Equation

(KS3, Year 8)

## The Lesson

The slope of a line is its steepness. It is how far up a line goes compared to how far across it goes. The line below has a slope of**2**because it goes up 2 units for every 1 unit it goes across.

A line can be represented by a linear equation. We can find the slope from a linear equation.

## Real Examples of Finding the Slope from a Linear Equation

Finding the slope of a line from a linear equation is easy. Here are some linear equations, which represent lines. We show how to find the slope from the linear equation.-
The slope of
**y = 2x + 1**is**2**.

Look at the number in front of the**x**(called the coefficient of x). This is the slope. A slope of 2 means that the line will go up by 2 when it goes across by 1. -
The slope of
**y = −3x + 3**is**−3**.

The number in front of the x is negative. This means the line slopes**downwards**. A slope of −3 means that the line will go down by 3 when it goes across by 1. -
**y = 2**is a horizontal line. It has a slope of**0**.

**y = 2**does not have an**x**in it. We can imagine there is an invisible**0**in front of the x which gets rid of it. A slope of 0 means that the line will neither go up nor down when it goes across by 1.

## Postive And Negative Slopes

A positive slope means the line slopes up and to the right:A negative slope means the line slopes down and to the right:

## Fractional Slope

Slope can be a fraction, such as ½ and ¾. An improper fraction is positive, but less than 1. A slope of 1 gives a 45° line. A fractional slope is less steep than this:## Zero Slope And Undefined Slope

A line that goes straight across has zero slope:A line that goes straight across has an undefined slope:

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