rate of change and slope
· calculate the rate of change or slope of a linear function given information as sets of ordered pairs, a table, or a graph.
· apply the slope formula.
we experience slopes every day. think about biking down a hill or climbing a set of stairs. both the hill and the stairs have a slope. that means that as we travel along them, we are moving in two directions at the same time—sideways, and either up or down. in conversation, we use words like gentle or steep to describe the slope of the ground or an object. along a gentle slope, most of the movement is horizontal. along a steep slope, the vertical movement is greater.
the mathematical definition of slope is very similar to our everyday one. in math, slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. the vertical change between two points is called the rise, and the horizontal change is called the run. the slope equals the rise divided by the run: . this simple equation is called the slope formula.
the slope formula is often shortened to the phrase “rise over run.” although it sounds simple, the slope formula is a powerful tool for calculating and comparing the steepness of landscapes, structures, and lines.
Given: Coby is four years older than CoraCora (a): xCoby (b): x+4Average of their ages: 19
To solve for average, add the the given values then divide by the total number of items. In this problem, add the ages then divide by the total number of people.Average (or Mean) = (a + b)/2
[(x) + (x+4)]/2 = 19
x + x +4 = (19)(2)
Find x, Cora's age:
2x + 4 = 38
2x = 38 - 4
2x/2 = 34/2
x = 17 ⇒ Cora's ageCora is 17 years old.
To solve for Coby's age, x+4 when x=17:
17 + 4 = 21
Coby is 21 years old.
(17 + 21)/2 = 19
38/2 = 19
19 = 19 (True)