Write an equation of the line that passes through the points (0, 1) and (−2, −5).
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 (0, 1) and (−2, −5) is y - 3x -1 = 0
Let us proceed step by step to find the equation of the line.
Let us consider the given points (0, 1) and (−2, −5).
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).
Hence, on substituting the given points in the equation of a line, we get
y - 1 = m (x - 0)
m = (y2 - y1) / (x2 - x1)
m = (-5 - 1) / (-2 - 0)
m = -6 / -2 = 3
Substituting the value of m in y - 1 = m (x - 0), we get
y - 1 = 3 (x - 0)
y - 1 = 3x
y = 3x + 1
y - 3x -1 = 0
You can use Cuemath's online Equation of Line calculator to find the equation of a line.