Two-Points Equation Game
To find a linear equation from two points, first, calculate the slope. Next, use the slope and one of the points to find the y-intercept (b) by solving the slope-intercept equation (y=mx+b) for b. Finally, write the equation in slope-intercept form y=mx+b using the calculated slope and y-intercept. Scroll down the page for a more detailed explanation.
 
This game is designed to help you master the process to determine a linear equation from two points on the line. If you get an answer wrong, it will show you the correct solution.
 

Two-Point to Equation

Given two points, find the linear equation (y = mx + b). Enter answers as integers or simplified fractions.

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Given the following points:

Point 1 =

Point 2 =

Find the equation (y = mx + b):

y =

x + -

Check Next

Back to Menu

 

How to Play the Two-Points Equation Game
This game is designed to help you master the process of determining a linear equation from the two points on the line.
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 two points on a line. Find the equation of the line
   
3. Enter Your Answer: Enter in the values for m and b.
   
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 linear equation from two-points on the line
Step 1: Calculate the slope \( (m) \)

1. Label your two points as \( (x_{1},y_{1}) \) and \( (x_{2},y_{2}) \).
   
2. Use the slope formula: \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \).
   
3. Substitute the coordinates of your two points into the formula and simplify to find the slope, \(m\).
    
   

Step 2: Find the y-intercept \( (b) \)

1. Use the slope-intercept form of a linear equation: \(y=mx+b\).
   
2. Substitute the slope \( (m) \) you found in Step 1 and the coordinates of one of the original points \((x,y)\) into the equation.
   
3. Solve the equation for \(b\).
    
   

Step 3: Write the final equation
Now that you have both the slope \( (m) \) and the y-intercept \( (b) \), write the final equation in slope-intercept form: \(y=mx+b\).
For example, if you found \( m=2\) and \( b=5 \), the final equation would be \(y=2x+5\).
 

The video gives a clear, step-by-step approach to find the linear equation from two-points on the line.

• Show Video

 

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