Point-Slope Form

Algebra 1 Tutorial

Point-Slope Form


In this tutorial, we will discover how to find the equation of a line using the Point-Slope formula.

Sample Problem

What is the equation of a line that crosses through (5,7) and has a slope of 2?


Step One: Understanding the Problem
The problem asks for the equation of a line that crosses through Point A at (5,7) and has a slope of two. The two things that we must take away from this question in order to put it into Point-Slope form is the point and the slope.

The problem states that the line crosses through Point A at (5,7). This means Point A=(5,7)

The problem states that the line has a slope of two. This means Slope=2

Step Two: Understanding the Point-Slope Formula
The formula for Point-Slope form is: y-y1=m(x-x1)

This means, in order to put the problem into Point-Slope form, we must know where to put the slope and the coordinate(point) into the equation.

“m” is the variable for slope, so m=2.
x1 is the variable for the x-value of your coordinate. So, x1=5.
y1 is the variable for the y-value of your coordinate. So, y1=7

Step Three: Solving the Problem
In order to solve the problem, we must first fill in our variables into the Point-Slope formula.

y-y1=m(x-x1) : Point-Slope Formula
y-y1=2(x-x1) : Fill in the slope for “m”
y-y1=2(x-7) : Fill in the x-value for “x1”
y-7=2(x-7) : Fill in the y-value for “y1”

The next step to solving the problem is to simplfy your equation using the order of operations.

y-7=2(x-7) : Your Equation
y-7=2x-14 : Use the Distributive Property to distribute the 2 into the parenthesis.
y=2x-7 : Add 7 to both sides of the equation

Your finished equation is y=2x-7

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