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Finding the Slope from a Linear Equation

(KS3, Year 8)

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. The slope of the line is 2 because it goes up 2 units for every 1 it goes across

The slope of the line is 2 because it goes up 2 units for every 1 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.

Lesson Slides

A linear equation (in slope-intercept form) is given in the form below: y = mx + c The m gives the slope of the line. The slider below explains why the m in a linear equation gives the slope:

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: $fractional slope$