lesson
Updated 6 days ago · 2 views
Imagine your older sister is always exactly 3 years older than you. When you are 7, she is 10; when you are 12, she is 15.
No matter how old you get, her age is always found by doing the exact same addition: your age plus 3.
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 in symbols as the equation y=x+a, where the constant number a never changes.
📊A visual rule breakdown card titled 'The Additive Rule: y = x + a'. Shows three horizontal boxes with arrows connecting them: [Input x] -> [+ a (Constant Amount Added)] -> [Output y]. Below the diagram, two labeled callout examples appear side by side: Left box shows 'y = x + 3' (adds 3), Right box shows 'y = x - 2' (adds -2). Clean layout on white background (#ffffff) with soft borders (#e6e6e6) and text color (#1e2945).
How do we take an equation like y=x+3 and turn it into a picture on a grid?
Step 1: Make a Table of Values
To graph any rule, start by choosing a few values for x, including negative numbers and zero, then calculate each matching y value.
Each pair of x and y values forms an ordered pair (x,y) that marks one exact location on the coordinate plane.
📊An interactive-looking visual table card for y = x + 3. Columns: 'x (Input)', 'Rule: x + 3', 'y (Output)', and 'Point (x, y)'. Rows show: -2 -> -2 + 3 = 1 -> (-2, 1); 0 -> 0 + 3 = 3 -> (0, 3); 1 -> 1 + 3 = 4 -> (1, 4); 3 -> 3 + 3 = 6 -> (3, 6). The row with x = 0 is highlighted in light blue with a badge saying 'y-intercept (0, 3)'. Sleek modern UI design, crisp typography.
Now that we have our list of coordinate points, what happens when we plot them together?