To derive the equation of a line in slope-intercept form, you need two pieces of information: the slope of the line (m) and the y-intercept (b).
The slope-intercept form of a line is given by the equation:
y = mx + b
where:
- m is the slope of the line
- b is the y-intercept of the line
- (x, y) are the coordinates of a point on the line
To derive the equation of a line in slope-intercept form, you first need to find the slope of the line. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Once you have the slope of the line, you can substitute it and one of the points on the line into the slope-intercept form equation to determine the y-intercept.
Finally, plug in the slope and y-intercept values into the equation y = mx + b to obtain the equation of the line in slope-intercept form.
Derive The equation of the line and slope intercept form
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