Exploring y = mx + b

This activity corresponds to the topic of Functions, in which you will manipulate the parameters m and b to understand how each one transforms the graph of a linear function.

Move the m and b controls, analyze the changes in the graph, answer the challenges, and check your predictions before moving the sliders.

Current Function

y = 1x + 0

Y-Intercept

(0, 0)

Slope (m) 1

Controls the line's steepness

Intercept (b) 0

Shifts the line vertically

Challenge: predict before moving

1. If m = 0, will the line be horizontal? — Click to verify

2. If m is negative, does the line go down from left to right? — Click to verify

3. Change b = 5. At what point does the function cross the Y-axis? — Click to verify

4. What values of m and b generate y = −2x + 3? — Click to activate this function

Table of Values (x from −3 to 3)