Algebra

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# Point Slope Form

## 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

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

Problem 2:
A line passes through points (2, 4) and (8, 16). Write the equation of the line in point slope form.
Solution:
First we must find the slope.
m = y2 – y1x2 – x1
m = 16 – 48 – 2 = 12/6 = 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)
The equation of the line is y – 4 = 2(x – 2).

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