Write an equation of the line that passes through the given two points: (1, 0) and (3, 4)
A two-point form of the equation is used when two different points on the line are known.
Answer: The general equation of the line is y = 2x - 2
This equation can easily be simplified to any of the forms of the equation like the slope-intercept form, so as to calculate the intercept value by comparison.
Let the given points are (x1, y1) = (1, 0) and (x2, y2) = (3, 4).
Therefore, applying the slope-intercept form of the equation,
⇒ y - y1 = m (x - x1)
⇒ m = slope formula = (y2 - y1) / (x2 - x1)
Slope of the line = m = (4 - 0) / (3 - 1) = 4 / 2 = 2
You can find thye slope using the slope calculator.
Using the point (1, 0), let's write the equation of the line.
(y - 0) = m (x - 1) [Since, (y2 - y1) / (x2 - x1) = m]
⇒ y = 2(x - 1)
⇒ y = 2x - 2
Thus, the equation of the line passing through the points (1, 0) and (3, 4) is y = 2x - 2.