Unit 3, Lesson 6
More Linear Relationships
Grade 8
6.1
Warm-up
What do you notice? What do you wonder?
6.2
Activity
Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days.
After day 1, Lin reaches page 70, which matches the point she made on her graph. After day 4, Lin reaches page 190, which does not match the point she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan. Why doesn’t Lin’s reading progress match her graph?
Student Lesson Summary
Lines drawn on a coordinate plane have a slope and a vertical intercept. The vertical intercept indicates where the graph of the line meets the vertical axis. Since the vertical axis is often referred to as the -axis, the vertical intercept is often called the “-intercept.” A line represents a proportional relationship when the vertical intercept is 0.
Here is a graph of a line showing the amount of money paid for a new cell phone and monthly plan.
The vertical intercept for the graph is at the point and means the initial cost for the phone was \$200.
A slope triangle connecting the two points and can be used to calculate the slope of this line. The slope of 50 means that the phone service costs \$50 per month in addition to the initial \$200 for the phone.
The vertical intercept is the point where the graph of a line crosses the vertical axis.
The vertical intercept of this line is or just -6.