Finding the Slope from a Linear Equation in Slope-Point Form
(KS3, Year 9)
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.
Beware
Be Careful
In this lesson, we have said that the slope is given by the number in front of the brackets with the x in it. 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).
Note
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:Worksheet
This test is printable and sendable