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## Algebra 1

### Course: Algebra 1>Unit 5

Lesson 4: Point-slope form

# Point-slope form review

Review point-slope form and how to use it to solve problems.

## What is point-slope form?

Point-slope is a specific form of linear equations in two variables:
y, minus, start color #1fab54, b, end color #1fab54, equals, start color #ed5fa6, m, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, a, end color #11accd, right parenthesis
When an equation is written in this form, start color #ed5fa6, m, end color #ed5fa6 gives the slope of the line and left parenthesis, start color #11accd, a, end color #11accd, comma, start color #1fab54, b, end color #1fab54, right parenthesis is a point the line passes through.
This form is derived from the slope formula.

## Finding point-slope equation from features or graph

### Example 1: Equation from slope and point

Suppose we want to find the equation of the line that passes through left parenthesis, start color #11accd, 1, end color #11accd, comma, start color #1fab54, 5, end color #1fab54, right parenthesis and whose slope is start color #ed5fa6, minus, 2, end color #ed5fa6. Well, we simply plug start color #ed5fa6, m, equals, minus, 2, end color #ed5fa6, start color #11accd, a, equals, 1, end color #11accd, and start color #1fab54, b, equals, 5, end color #1fab54 into point-slope form!
y, minus, start color #1fab54, 5, end color #1fab54, equals, start color #ed5fa6, minus, 2, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, 1, end color #11accd, right parenthesis

### Example 2: Equation from two points

Suppose we want to find the line that passes through the points left parenthesis, 1, comma, 4, right parenthesis and left parenthesis, 6, comma, 19, right parenthesis. First, we use the two points to find the slope:
Now we use one of the points, let's take left parenthesis, start color #11accd, 1, end color #11accd, comma, start color #1fab54, 4, end color #1fab54, right parenthesis, and write the equation in point-slope:
y, minus, start color #1fab54, 4, end color #1fab54, equals, start color #ed5fa6, 3, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, 1, end color #11accd, right parenthesis
Problem 1
• Current
Write the point-slope equation of the line that passes through left parenthesis, 7, comma, 3, right parenthesis whose slope is 2.

Want to try more problems like this? Check out this exercise.

## Finding features and graph from point-slope equation

When we have a linear equation in point-slope form, we can quickly find the slope of the corresponding line and a point it passes through. This also allows us to graph it.
Consider the equation y, minus, start color #1fab54, 1, end color #1fab54, equals, start color #ed5fa6, 2, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, 3, end color #11accd, right parenthesis. We can tell that the corresponding line passes through left parenthesis, start color #11accd, 3, end color #11accd, comma, start color #1fab54, 1, end color #1fab54, right parenthesis and has a slope of start color #ed5fa6, 2, end color #ed5fa6. Now we can graph the line:
Problem 1
• Current
What is the slope of the line y, minus, 5, equals, minus, 4, left parenthesis, x, minus, 8, right parenthesis?
The line passes through which point?