Algebra

##### Related Lessons

- Adding and Subtracting Scientific Notation
- Adding Fractions
- Algebra Calculators
- Arithmetic Sequence
- Average Rate of Change
- Change of Base Formula
- Cm to M
- Commutative Property of Addition
- Completing the Square
- Cross Product Calculator
- Determinant Calculator
- Determinant of a Matrix
- Difference of Squares
- Discriminant
- Divisibility Rule for 7
- Dot Product Calculator
- Eigenvalue Calculator
- Eigenvector Calculator
- Equation of a Circle
- Even Numbers
- Exponent Rules
- Factorial Calculator
- Fractional Exponents
- How to Find the Median
- Interval Notation
- Matrix Addition
- Matrix Subtraction
- Midpoint Formula
- Multiplying Negative Numbers
- Negative Exponents
- Odd Numbers
- One to One Function
- Partial Fraction Decomposition Calculator
- Point Slope Form
- Properties of Multiplication
- Rationalize the Denominator
- Rectangular to Polar Calculator
- Reflexive Property
- Round to the Nearest Tenth
- RREF Calculator
- Slope Calculator
- Slope Intercept Form
- Standard Form
- Summation Calculator
- Vertex Form

Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# 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 – y _{1} = m(x – x_{1})**

Where *(x _{1}, y_{1})* 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 – x _{1})*. We now have y – y

_{1}= mx – mx

_{1}.

2. Add y

_{1}to both sides of the equation. We now have y = mx – mx

_{1}+ y

_{1}.

3. Plugging in the coordinates

*x*and

_{1}*y*and simplifying/combining terms gives us slope intercept form

_{1}*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 – y1}⁄_{x2 – x1}

m = ^{16 – 4}⁄_{8 – 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).**

Result :

Worksheet 1

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Cheat sheet

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