Parallel Equations Game (Standard Form)
To find the equation of a parallel line from a given line in standard form (Ax+By=C) through a given point: Take the Ax+By part of the original equation, substitute the new point’s coordinates into it, and set this equal to a new constant (C’). to find the final equation (Ax+By=C’). 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 parallel 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 Parallel Line (Slope-Intercept)
Equation of a Parallel Line (Standard Form)

 

Parallel Line Equations

Find the equation in Standard Form `Ax + By = C`.
Ensure A is positive and gcd(A,B,C) = 1.

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Find the equation of a line parallel to:

and passing through the point:

Enter your equation (Ax + By = C):

x + y =

Check Next

Back to Menu

 

How to Play the Parallel Equations Game (Standard Form)
This game is designed to help you master the process to determine the equation of a line parallel 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 parallel 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 parallel line
To find the equation of a parallel line from a given line in standard form (Ax+By=C) through a given point: Take the Ax+By part of the original equation, substitute the new point’s coordinates into it, and set this equal to a new constant (C’). to find the final equation (Ax+By=C’).
Method 1: Keep A and B, find C (most direct)

1. Identify A and B:
   Look at the standard form equation Ax+By=C and identify the values for A and B.
   
2. Substitute the point:
   Take the given point (x₁,y₁) and plug its coordinates into the expression Ax+By
   .
3. Calculate the new C: The result of the substitution is the new constant, C’. So, C’=Ax₁+By₁.
   
4. Write the new equation: The equation of the parallel line is Ax+By=C’ (Simply the equation when possible).
    
   

Method 2: Use slope-intercept form

1. Find the slope (m):
   Rearrange the original standard form equation into slope-intercept form y=mx+b to find the slope, m.
   
2. Use the parallel slope:
   Parallel lines have the same slope, so the new line’s slope m_parallel is the same as the original line’s slope.
   
3. Use the point-slope form:
   Use the point-slope formula, y-y₁ = m_parallel(x - x_₁), substituting the slope and the coordinates of the given point.
   
4. Simplify to standard form:
   Simplify the point-slope equation and rearrange it into the standard form Ax+By=C.
    
   

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

• Show Video

 

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