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.
Explanation:
Let us consider the given points (2, 2) and (3, 4).
As we know that the equation of a line passing through the points (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)) is given by y - \(y_{1}\) = m (x - \(x_{1}\)).
Here, m is the slope given by the formula m = (\(y_{2}\) - \(y_{1}\)) / (\(x_{2}\) - \(x_{1}\))
Check out Cuemath's Slope Calculator that helps you to calculate the slope.
Hence on substituting the points (2, 2) in the equation of a line, we get
y - 2 = m (x - 2)
m = (\(y_{2}\) - \(y_{1}\)) / (\(x_{2}\) - \(x_{1}\))
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 a line.