A Line Passes through (2, 8) and (4, 12). Which Equation Best represents the Line?
The general equation of a straight line can be written as y = mx + c where m is the slope and c is the y-intercept.
Answer: The equation of a line passing through the points (2, 8) and (4, 12) is y = 2x + 4.
Let us proceed step by step to find the equation of the line.
Let us consider the given points (2, 8) and (4, 12).
As we know that the equation of a line passing through the points (x1, y1) and (x2, y2) is given by y - y1 = m (x - x1).
Try using Cuemath's Slope Calculator that helps you to calculate the slope in a few seconds.
Hence on substituting the given points in the equation of a line, we get
y - 8 = m (x - 2)
m = (y2 - y1) / (x2 - x1)
m = (12 - 8) / (4 - 2)
m = 4 / 2
m = 2
Substituting value of m in y - 8 = m (x - 2), we get
⇒ y - 8 = 2 ( x - 2 )
⇒ y - 8 = 2x - 4
⇒ y = 2x + 4
You can use Cuemath's online Equation of Line calculator to find the equation of line.