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 in Slope-Point Form
Finding the slope of a line from a linear equation in slope-point form 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 − 4 = 2(x − 1) is 2.
Look at the number in front of the brackets with the x in it. This is the slope.
A slope of 2 means that the line will go up by 2 when it goes across by 1.
slope of y − 1 = −3(x − 3) is −3.
The number in front of the brackets 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.
A linear equation (in slope-point form) is given in the form below:
y − y1 = m(x − x1)
The m gives the slope of the line.
The slider below explains why the m in a linear equation gives the slope:
In this lesson, we have said that the slope is given by the number in front of the brackets with the x
This is true as long as the x
in the brackets is positive
and doesn't have another number in front of it.
For example, consider the linear equations shown below:
The x has a − sign in front of it:
y − 1 = 2(−x − 1)
The slope would be −2.
The x has a number front of it:
y − 1 = 2(3x − 1)
The slope would be 6 (2 × 3).
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:
Zero Slope And Undefined Slope
A line that goes straight across has zero slope:
A line that goes straight across has an undefined slope: