Perpendicular Equations Game (Slope-Intercept)
To find the equation of a perpendicular line through a point, find the negative reciprocal of the original line’s slope, then use the point-slope form (y-y₁=m(x-x₁)) or slope-intercept form (y=mx+b) to solve for the new equation. Scroll down the page for a more detailed explanation.
 
This game is designed to help you master the process to determine the equation of a line perpendicular to a given line and passing through a specific point. The given equation is in slope-intercept form. If you get an answer wrong, it will show you the correct solution.
 

Equation of a Perpendicular Line (Slope-Intercept)
Equation of a Perpendicular Line (Standard Form)

 

Perpendicular Lines

Find the equation of a line perpendicular to the given line and passing through the point.

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Perpendicular to:

Passing through:

Enter your equation (y = mx + b):

y = x + -

Check Next

Back to Menu

 

How to Play the Perpendicular Equations Game (Slope-Intercept)
This game is designed to help you master the process to determine the equation of a line perpendicular to a given line and passing through a specific point. The given equation is in slope-intercept form.
Here’s how to play:

1. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
2. Look at the Problem: You’ll be given the equation of a line in slope-intercept form and a point. Find the equation of the line perpendicular to the given line and passing through the given point.
   
3. Enter Your Answer: Enter in the values for m and b. (Include the negative sign when needed)
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
   
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to find the equation of a perpendicular line
Step 1: Find the slope of the new line
If the original line’s slope is m₁, the perpendicular slope m₂ is the negative reciprocal.
To find the negative reciprocal, flip the fraction of the original slope and change its sign.
Step 2: Use the point-slope form
The point-slope form is y-y₁=m(x-x₁), where m is the new slope and (x₁,y₁) is the given point.
Substitute the new slope and the coordinates of the given point into the equation.
Step 3: Alternatively, use the slope-intercept form
The slope-intercept form is y=mx+b.Substitute the new slope (m) into the equation.
Substitute the coordinates of the given point (x,y) into the equation to solve for b.
 

The video gives a clear, step-by-step approach to find the equation of a line perpendicular to a given line passing through a given point.

• Show Video

 

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