Writing the equation of the line through two given points (2, 2) and (3, 4).
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 through the points (2,2) and (3,4) is y - 2x + 2 = 0.
Let us proceed step by step to find the equation of the line.
Let us consider the given points (2, 2) and (3, 4).
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).
Check out Cuemath's Slope Calculator that helps you to calculate the slope.
Hence on substituting the given points in the equation of a line, we get
y - 2 = m (x - 2)
m = (y2 - y1) / (x2 - x1)
m = (4 - 2) / (3 - 2)
m = 2 / 1 = 2
Substituting the value of m in y - 2 = m (x - 2), we get
y - 2 = 2 (x - 2)
y - 2 = 2x - 4
y = 2x - 2
y - 2x + 2 = 0
You can use Cuemath's online Equation of Line calculator to find the equation of line.