Equation of a Straight Line

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1- Equation of a Straight Line

2a- A line AB is parallel to the X-axis when all of its points are at a constant distance from it.

2b- That equation would be y = k since all points whose ordinate is k would lie on that line.

3a- A line AB is parallel to the Y-axis when all of its points are at a constant distance from it.

3b- That equation would be x = k since all points whose abscissa is k would lie on that line.

4a- The slope is the vertical difference of two points divided by their horizontal difference.

4b- For horizontal lines y2 = y1, numerator = 0, and the slope is 0.

4c- For vertical lines: x2 = x1, denominator = 0, and the slope is undefined.

5a- This is the expression of the point-slope equation of a straight line. You need any point of the line and its slope.

5b- You can have more than one expression or equation, because you can always consider more than one point.

6a- In this example, point 1 is (-2, 1) and point 2 is (3, 5).

6b- The slope of this line is always 4/5, no matter which points or order we take.

6c- These two expressions represent the same line and just show different points.

7- The slope-intercept form takes into account the slope of a line and the y-intercept.

8- In this example, our y-intercept is 5, and our slope is 2.

9- In the general form we have a different approach. We can express the same line in many ways. We have coefficients A, B and C.

9a- The slope is the negative coefficient of x divided by the coefficient of y, that is --A/B.

9b- The y-intercept is the negative constant divided by the coefficient of y, that is --C/B.

9c- With the general form we can easily find the slope of a line and its y-intercept.

10- In this example the coefficient of x is 3, the coefficient of y is 7 and the constant is 5. Thus, the slope is -3/7 and the y-intercept is -5/7.

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