# What is the relationship between rate of change and slope?

## What is the relationship between rate of change and slope?

Explanation: Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates.

## Which line has the greatest slope?

If you imagined these lines to be hills, you would say that line B is steeper than line A. Line B has a greater slope than line A. Next, notice that lines A and B slant up as you move from left to right. We say these two lines have a positive slope….

x | y |
---|---|

−1 | −5 |

0 | 0 |

2 | 10 |

**What if the rate of change is not constant?**

A rate of change measures how quickly a measured quantity, such as position, is changing. time will be a straight line, and you can find the rate of change by calculating the slope of the line. If the rate of change is not constant, a graph of the measured quantity vs. time will be curved instead of straight.

**What is the slope of the line 3x y 7?**

Using the slope-intercept form, the slope is −3 .

### How is the slope of a line related to rate of change?

The slope of a line tells us how something changes over time. If we find the slope we can find the rate of change over that period. This can be applied to many real life situations. Take a look at the following graph.

### How to find the slope of a house?

Step 1: Write two ordered pairs: (19, 245,000) (In 2009 (19 years after 1990) the house is worth $245,000) Step 2: Use the slope formula to find the slope. Linda’s average annual rate of change if $9,182 dollars per year.

**How to find the slope of interval a?**

Step 1: Identify the two points that cover interval A. The first point is (0,0) and the second point is (1,6). Step 2: Use the slope formula to find the slope, which is the rate of change.

**How to find the annual rate of change?**

Find the average annual rate of change in dollars per year in the value of the house. Round your answer to the nearest dollar. (Let x = 0 represent 1990) For this problem, we don’t have a graph to refer to in order to identify the two ordered pairs.