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Welcome to our Math lesson on Review of the Linear Equations Concepts previously covered , this is the first lesson of our suite of math lessons covering the topic of Equation of Linear Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Review of the Linear Equations Concepts previously covered
We explained in the 9th chapter (and in tutorial 14.1 as well) that a straight line has an equation of the form
ax + by + c = 0
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
y = mx + n
or sometimes
y = kx + t
as well, where the coefficient m (or k) represents the gradient discussed in the previous tutorial, while the constant n (or t) represents the y-intercept of the line (as explained in tutorial 14.1).
Another thing we have explained in the 9th chapter was how to obtain the simplified form of the equation of a line from the general equation. Thus, isolating the variable y in the general equation of a line
ax + by + c = 0
we obtain
by = -ax - c
y = -a/b ∙ x - c/b
where the coefficient (gradient) m (or k) of the line is
m = k = -a/b
and the constant n (or t), which represents the y-intercept of the graph is
n = t = -c/b
For example, if we want to write the line
2x - 3y + 1 = 0
(where a = 2, b = -3 and c = 1) in the form
y = mx + n
we obtain
2x - 3y + 1 = 0
2x + 1 = 3y
2/3 x + 1/3 = 3y/3
y = 2/3 x + 1/3
In this way, we obtain the new coefficient and constant of the line
m = 2/3 and n = 1/3
Example 1
Write the following lines in the form y = mx + n.
- 5x + 2y - 3 = 0
- x - 4y + 2 = 0
Solution 1
- We have a = 5, b = 2 and c = -3. Given that
m = k = -a/b
we obtain for the coefficient (gradient) m after substitutions: m = -5/2
On the other hand, since n = t = -c/b
we obtain for the constant n after substitutions n = --3/2
= 3/2
Therefore, the simplified equation of the line 5x + 2y - 3 = 0 is y = -5/2 x + 3/2
- We have a = 1, b = -4 and c = 2. Given that
m = k = -a/b
we obtain for the coefficient (gradient) m after substitutions: m = -a/b
= -1/-4
= 1/4
On the other hand, since n = t = -c/b
we obtain for the constant n after substitutions n = -2/-4
= 2/4
= 1/2
Therefore, the simplified equation of x - 4y + 2 = 0 is y = 1/4 x + 1/2
More Equation of Linear Graphs Lessons and Learning Resources
Linear Graphs Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 14.3 | Equation of Linear Graphs | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 14.3.1 | Review of the Linear Equations Concepts previously covered | | |
| 14.3.2 | How to find the Equation of a Line? | | |
| 14.3.3 | Finding the Equation of a Line that Passes through Two Known Points | | |
| 14.3.4 | Finding the Equation of a Line from a given Graph | | |
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