We will discuss here about the meaning of equation of a straight line.
Let the straight line be PQ which passes through the origin (0, 0) and inclined at 45° with the positive direction of the x-axis. Let the points on the line PQ are (x\(_{1}\), y\(_{1}\)), (x\(_{2}\), y\(_{2}\)), (x\(_{3}\), y\(_{3}\)), etc.,
According to the definition of coordinates \(\frac{y_{1}}{x_{1}}\) = tan 45° = \(\frac{y_{2}}{x_{2}}\) = \(\frac{y_{3}}{x_{3}}\) = etc.,
Therefore, y\(_{1}\) = x\(_{1}\), y\(_{2}\) = x\(_{2}\), y\(_{3}\) = x\(_{3}\), etc.,
Thus, from the above explanation we conclude that for any point (x, y) on the line,
y-coordinate = x-coordinate
i.e., x = y, where (x, y) is any point on the line.
y = x is the equation of the straight line PQ.
Definition of the equation of a straight line:
The equation of a straight line is the common relation between the x-coordinate and y-coordinate of any point on the line.
Note: The coordinates of any point on the straight line satisfy the equation of the line.
Let the equation of a straight line y = 5x - 2. The point (1, 3) lies on the line y = 5x- 2 because (1, 3) satisfy the equation y = 5x – 2. Since by plugging 1 for x and 3 for y in the equation, we get 3 = 5(1) – 2 i.e., ⟹ 3 = 5 – 2 ⟹ 3 = 3, which is true.
But the point (2, 4) does not a lies on the line y = 5x- 2 because (2, 4) does not satisfy the equation y = 5x – 2.
Since by plugging 2 for x and 4 for y in the equation, we get 4 = 5(2) – 2 i.e., ⟹ 4 = 10 – 2 ⟹ 4 = 8, which is not true.
● Equation of a Straight Line
From Equation of a Straight Line to HOME
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Sep 15, 24 04:57 PM
Sep 15, 24 04:08 PM
Sep 15, 24 03:16 PM
Sep 14, 24 04:31 PM
Sep 14, 24 03:39 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.