What is the Equation of Straight line?

Asked by tusharparik15 days ago

What is the Equation of Straight line?

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15 days ago
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Mathematics - Equation of a Straight Line

The equation of a straight line describes the relationship between x and y coordinates on the line. There are several forms, but the most common is the slope-intercept form.

Slope-Intercept Form

The slope-intercept form of a straight line equation is: y = mx + b
Where:

  • y is the y-coordinate
  • x is the x-coordinate
  • m is the slope of the line (the rate of change of y with respect to x)
  • b is the y-intercept (the point where the line crosses the y-axis)

Point-Slope Form

Another useful form is the point-slope form:
y - y₁ = m(x - x₁)
Where:

  • (x₁, y₁) is a known point on the line
  • m is the slope of the line
This form is helpful when you know a point on the line and the slope.

General Form

The general form of a linear equation is:
Ax + By + C = 0
Where A, B, and C are constants, and A and B are not both zero. This form can be rearranged to find the slope and intercepts.

Example 1: Slope-Intercept Form

Find the equation of a line with a slope of 2 and a y-intercept of -3.
Using y = mx + b:
y = 2x - 3

Example 2: Point-Slope Form

Find the equation of a line passing through the point (1, 4) with a slope of -1.
Using y - y₁ = m(x - x₁):
y - 4 = -1(x - 1)
y - 4 = -x + 1
y = -x + 5

Study Tip: Understanding the relationship between the slope, y-intercept, and the equation of a line is crucial for graphing and solving linear equations. Practice converting between these forms.

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