Equation of Linear Graphs - Revision Notes
In addition to the revision notes for Equation of Linear Graphs on this page, you can also access the following Linear Graphs learning resources for Equation of Linear Graphs
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions |
|---|---|---|---|---|---|
| 14.3 | Equation of Linear Graphs |
In these revision notes for Equation of Linear Graphs, we cover the following key points:
- What are linear equations?
- What are the elements involved in linear equations?
- What is the general and simplified formula of a linear equation?
- How do we find the intercepts with the x- and y-axes?
- What is the gradient of a line? How do we find it?
- How do we find the equation of a line using the gradient?
- How do we find the equation of a line with two known points?
- How do we find the equation of a line from a given graph?
Equation of Linear Graphs Revision Notes
A straight line has an equation of the form
where a and b are coefficients and c is a constant.
When dealing with graphs, however, it is more appropriate to express a straight line in a new simplified form
or sometimes
where the coefficient m (or k) represents the gradient (the value of the slope), while the constant n (or t) represents the y-intercept of the line. The coefficient (gradient) m (or k) of the line is
and the constant n (or t), which represents the y-intercept of the graph is
The above formulas allow switching from one form of expressing a linear equation to the other.
From the definition of the gradient m, we know that
Rearranging this formula for y yields,
or
Expressing y0 - mx0 by a single letter (we usually take it as n), yields the simplified equation of a line
The x-intercept of a line for which the corresponding y-coordinate is zero (y0 = 0) is
and the y-intercept of the same line for which the corresponding x-coordinate is zero (x0 = 0) is
You don't need to remember the above formulas for the x-and y-intercepts. All you need to do is to substitute y = 0 in the line's equation to find the y-intercept and x = 0 to find the y-intercept.
Sometimes, the reverse problem is given, i.e. when the linear equation is unknown but we know two points of the line. These two points, say A(x1, y1) and B(x2, y2) help us find the equation of the line expressed in the form y = mx + n in two steps:
Step 1: Calculating the gradient m through the formula
Step 2: Substitute the value found in Step 1 and the coordinates of one of the known points in the equation of the line to find the constant c.
When no other information except the graph of a line is given, we first identify two distinct points with easily identifiable coordinates (it is better to use the intercepts with the axes though this is not always possible); then we find the gradient m. The last step involves the substitution of one of the known points in the general equation to find the constant n.
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- Continuing learning linear graphs - read our next math tutorial: Parallel, Perpendicular and Intersecting Graphs
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