Unit 5, Lesson 7
Translating to $y=mx+b$
Accelerated 7
7.1
Warm-up
The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.
Lines j, h, g, f, e graphed on grid. j is green with a negative slope, h is yellow and parallel to f which is black, h is 6 unit up from f. e is red and parallel to f and h. e is 2 unit below f. g is blue and has a more steep positive slope than h, f, and e.
- Which lines are images of line after a translation?
- For each line that is a translation of , draw an arrow on the grid that shows the vertical translation distance.
Student Lesson Summary
During an early winter storm, snow falls at a rate of inch per hour. The rate of change, , can be seen in both the equation and in the slope of the line representing this storm.
The time since the beginning of the storm and the depth of the snow is a linear relationship. This is also a proportional relationship since the depth of snow is 0 inches at the beginning of the storm.
Graph of line. Horizontal axis, time since beginning of storm in hours, scale 0 to 6, by 1’s. Vertical axis, depth of snow in inches, scale 0 to 9, by 1’s. Points on line include 0 comma 0, 2 comma 1 and 4 comma 2.
During a mid-winter storm, snow again falls at a rate of inch per hour, but this time there were already 5 inches of snow on the ground.
The rate of change, , can still be seen in both the equation and in the slope of the line representing this second storm.
The 5 inches of snow that were already on the ground can be graphed by translating the graph of the first storm up 5 inches, resulting in a vertical intercept at . It can also be seen in the equation .
This second storm is also a linear relationship, but unlike the first storm, is not a proportional relationship since its graph has a vertical intercept of 5.
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