Definition of Point Slope Form

Point slope form is a way of representing the equation of a line passing through a point. We can use it if we know any point along a line and the line's slope. Point slope form is given as:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is a point along the line, and m is the slope of the line.

Point Slope to Slope Intercept Form

We can convert point slope form to slope intercept form with some simple algebraic manipulation. Here's the how to do it:

1. Use the distributive property to multiply m through the quantity of (x - x₁). We now have y - y₁ = mx - mx₁.
2. Add y₁ to both sides of the equation. We now have y = mx - mx₁ + y₁.
3. Plugging in the coordinates x₁ and y₁ and simplifying/combining terms gives us slope intercept form y = mx + b.

Point Slope Form Practice Problems

Let's go through a couple of examples together to practice using point slope form.

Practice Problem 1

A line passes through (1, 2) and has a slope of 5. Write the equation of the line in point slope form.

Solution:

1. We have a point and the slope, let's plug them into the formula.
   y - 2 = 5(x - 1)
2. The equation of the line is y - 2 = 5(x - 1).

Practice Problem 2

A line passes through points (2, 4) and (8, 16). Write the equation of the line in point slope form.

Solution:

1. First we must find the slope.
   m = ^{(y₂ - y₁)}⁄_{(x2 - x1)}
   m = ^{(16 - 4)}⁄_{(8 - 2)} = ¹²/₆ = 2
2. We will use the first given point with the slope we just found to get our point slope form equation.
   y - 4 = 2(x - 2)
3. The equation of the line is y - 4 = 2(x - 2).