Perpendicular Equations Game (Standard Form)
To find the equation of a perpendicular line, first convert the given standard form line (ax+by+c=0) to slope-intercept form (y=mx+b) to find its slope (m). Next, find the negative reciprocal of that slope to get the new slope for the perpendicular line. Finally, use the new slope and the given point in the point-slope form y-y₁=m(x-x₁) and convert it to standard form to find the final 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 standard 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 (in standard form) 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 (Ax + By = C):

x + y =

Check Next

Back to Menu

 

How to Play the Perpendicular Equations Game (Standard Form)
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 standard 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 standard 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
Method 1: Interchange A and B, negate, find C (most direct)
To find the perpendicular line’s equation from a given standard form line (Ax+By=C) through a point (x₁,y₁) directly, swap the coefficients of x and y, negate one of them, and then use the given point to find the new constant. The perpendicular line’s equation will be in the form Bx-Ay=K (or -Bx+Ay=K), where you substitute the given point into the equation to solve for K.
Step 1: Find the form of the perpendicular line
The given line is in the standard form Ax+By=C.
The new perpendicular line will have the form Bx-Ay=K or -Bx+Ay=K. For simplicity, use Bx-Ay=K.
Step 2: Substitute the given point to find the new constant (K)
You are given a point (x₁,y₁) that the new line must pass through.Substitute x₁ for x and y₁ for y in the equation Bx-Ay=K.
Solve the resulting equation for K.The equation becomes Bx-Ay=K, where K is the value you just found.
Step 3: Write the final equation
The final equation for the perpendicular line is Bx-Ay=K.
 

Method 2: Use slope-intercept form
Step 1: Find the slope of the given line
Rewrite the standard form equation, ax+by+c=0, into slope-intercept form, y=mx+b.
Isolate y to find the slope, m.
Step 2: Find the slope of the perpendicular line
The slope of a perpendicular line is the negative reciprocal of the original slope.
To find the negative reciprocal, flip the original slope’s fraction and change its sign
Step 3: Use the new slope and the given point to find the equation
Use the point-slope form of a linear equation: y-y₁=m(x-x₁).
Substitute the coordinates of the given point (x₁,y₁) and the new perpendicular slope (m) into the equation.
Simplify the equation, first into slope-intercept form (y=mx+b), and then into standard form (Ax+By=C).
 

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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