lesson
Updated 6 days ago · 2 views
If your older sister is 3 years older than you, she will always be 3 years older — whether you are 10, 25, or 80.
No matter how old you get, you just add 3 to your age to find hers.
How do mathematicians describe a pattern where you always add the exact same number?
What Is an Additive Relationship?
An additive relationship is a rule where you find the output value (y) by adding a fixed number (a) to the input value (x).
We write this rule algebraically as y=x+a, where a is called a constant because its value never changes.
📊An interactive-style visual diagram explaining the additive relationship y = x + 3. On the left, an input box showing values x = 2, 5, 8. In the center, a vibrant function machine labeled '+ 3 (constant)'. On the right, output values y = 5, 8, 11. Below, three horizontal comparison bars show: Row 1: 2 + 3 = 5 (difference: 5 - 2 = 3), Row 2: 5 + 3 = 8 (difference: 8 - 5 = 3), Row 3: 8 + 3 = 11 (difference: 11 - 8 = 3). Use clean cards with light background (#f8f9fa), blue highlights (#2563eb), and clear bold text.
To check if a table is additive, subtract the input from the output: y−x must give the same constant value for every pair.
What happens when we plot these pairs as coordinates on a grid?
Graphing Additive Rules
When the input x is 0, the equation y=0+a tells us that y must equal a.
This means the line crosses the vertical y-axis at the point (0,a), which is called the y-intercept.
📊A clean 2D coordinate grid showing the graph of y = x + 3. The x-axis goes from 0 to 6 and y-axis from 0 to 8. Plot the points (0, 3), (1, 4), (2, 5), and (3, 6) connected by a solid blue line. Highlight the point (0, 3) on the y-axis with a pulsing yellow circle labeled 'y-intercept (0, 3)'. Clearly show that the line does NOT pass through the origin (0, 0), with a small red 'X' at (0, 0) and a label 'Does not pass through (0, 0)'.