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Finding the Slope from a Linear Equation in General Form
(KS3, Year 9)
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.
How to Find the Slope from a Linear Equation in General Form
A linear equation (in general form) is given in the form below:The a, b and c do not immediately tell you anything about the line (such as its slope or y-intercept). But it can be converted to a form which does tell you about the line. For example, the slope-intercept form gives the slope and y-intercept.
It is the m in the slope-intercept form that tells you the slope. Once we know the slope-intercept form, we can read off the number in front of the x (the m) to find the slope. We can use algebra to convert the general form into the slope-intercept form:
Comparing this with y = mx + c, we see that the slope is −^{a}⁄_{b}. Read more about converting a linear equation in general form to slope-intercept form
A Real Example of Finding the Slope from a Linear Equation in General Form
Finding the slope of a line from a linear equation in general form is easy.Question
Find the slope of the line given by the linear equation shown below.Step-by-Step:
1
Find the number in front of the x. In our example, the number in front of the x is 4.
4x + 2y + 2 = 0
2
Find the number in front of the y. In our example, the number in front of the y is 2.
4x + 2y + 2 = 0
3
Divide the number from Step 1 (4) by the number from Step 2 (2).
4 ÷ 2 = 2
4
Answer:
The slope is −2.More Examples of Finding the Slope of a Line from Linear Equations
All of the linear equations we have seen in this lesson have been in general form (ax + b + c = 0). There are other forms of linear equation. You must be able to find the y-intercept in all forms of linear equation.-
You need to be able to find the slope of a linear equation in slope-intercept form:
Read more about finding the slope from a linear equation in slope-intercept form -
You need to be able to find the slope of a linear equation in slope-point form:
Read more about finding the slope from a linear equation in slope-point form
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:
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