Lesson 8: Translating to $y=mx+b$

Translating to $y=mx+b$

Student Summary

During an early winter storm, snow falls at a rate of $\frac12$ inch per hour. The rate of change, $\frac12$ , can be seen in both the equation $y=\frac12x$ 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.

During a mid-winter storm, snow again falls at a rate of $\frac12$ inch per hour, but this time there were already 5 inches of snow on the ground.

Graph of 2 lines. Points plotted on one line include 2 comma 6 and 4 comma 7. Points plotted on other line include 2 comma 1 and 4 comma 2. Arrows drawn between points.

The rate of change, $\frac12$ , 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 $(0,5)$ . It can also be seen in the equation $y=\frac12x+5$ .

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.

Visual / Anchor Chart

Standards

Building On

8.G.1

8.G.A.1

8.G.1.c

8.G.A.1.c

8.G.1.c

8.G.A.1.c

Addressing

8.EE.B