Vertical Translations of Linear Graphs
Vertical translations of linear graphs is a Grade 8 math concept in Illustrative Mathematics Chapter 3: Linear Relationships. Students learn that the graph of y = mx + b is a vertical shift of the proportional relationship y = mx, moved up by b units if b is positive or down if b is negative.
Key Concepts
The graph of a linear relationship $y = mx + b$ is a vertical translation of the graph of the proportional relationship $y = mx$. The graph is shifted vertically by $b$ units. If $b 0$, the shift is upward. If $b < 0$, the shift is downward.
Common Questions
What is a vertical translation of a linear graph?
A vertical translation shifts a linear graph up or down without changing its slope. The graph of y = mx + b is the graph of y = mx shifted vertically by b units.
How does the value of b affect a linear graph?
The constant b in y = mx + b is the y-intercept and determines the vertical shift. A positive b moves the line up; a negative b moves it down.
What is the difference between y = mx and y = mx + b?
y = mx is a proportional relationship passing through the origin, while y = mx + b adds a vertical translation of b units, shifting the line away from the origin.
Where is vertical translation of linear graphs covered in Illustrative Mathematics Grade 8?
This topic is in Chapter 3: Linear Relationships of Illustrative Mathematics, Grade 8.