What is the equation in point-slope form of the line passing through (0, 5) and (–2, 11)?
To find the equation of the line in point-slope form, you need the slope of the line and one point on the line.
Step 1: Find the slope (m)
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this case, the points are (0, 5) and (-2, 11). Substituting the values into the formula:
m = (11 - 5) / (-2 - 0)
m = 6 / -2
m = -3
The slope of the line is -3.
Step 2: Use the point-slope form
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
Using the slope (-3) and the point (0, 5), substitute the values into the equation:
y - 5 = -3(x - 0)
Simplifying:
y - 5 = -3x
This is the equation in point-slope form of the line passing through (0, 5) and (-2, 11).