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# Point Slope Form

## Point Slope Form Lesson

### 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.

INTRODUCING

### 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).
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