No.146 Graphs of Parallel Linear Functions
POINT
Linear functions with the same slope have parallel graphs. Changing the y-intercept shifts the line up or down.
Example
Complete the tables for \(y=\frac12x\) and \(y=\frac12x+4\), then draw both graphs.
① \(y=\frac12x\)
| x | -4 | -2 | 0 | 2 | 4 |
|---|---|---|---|---|---|
| y | -2 | -1 | 0 | 1 | 2 |
② \(y=\frac12x+4\)
| x | -4 | -2 | 0 | 2 | 4 |
|---|---|---|---|---|---|
| y | 2 | 3 | 4 | 5 | 6 |
Both lines have slope \(\frac12\), so they are parallel. The second graph is the first graph shifted 4 units upward.
TRY
TRY 1
Complete the tables for \(y=-2x\) and \(y=-2x+3\), then draw both graphs.
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y=-2x | |||||
| y=-2x+3 |
\(y=-2x:\ 4,2,0,-2,-4\)
\(y=-2x+3:\ 7,5,3,1,-1\)
The two lines have the same slope, so they are parallel.
\(y=-2x+3:\ 7,5,3,1,-1\)
The two lines have the same slope, so they are parallel.