The slope of each line segment is the same. This is because the points lie on the
Answers
Step-by-step explanation:
Introduction
The idea of slope is something you encounter often in everyday life. Think about rolling a cart down a ramp or climbing a set of stairs. Both the ramp and the stairs have a slope. You can describe the slope, or steepness, of the ramp and stairs by considering horizontal and vertical movement along them. In conversation, you use words like “gradual” or “steep” to describe slope. Along a gradual slope, most of the movement is horizontal. Along a steep slope, the vertical movement is greater.
Defining Slope
The mathematical definition of slope is very similar to our everyday one. In math, slope is used to describe the steepness and direction of lines. By just looking at the graph of a line, you can learn some things about its slope, especially relative to other lines graphed on the same coordinate plane. Consider the graphs of the three lines shown below:
m = 3
Substitute the values into the slope formula and simplify.
Answer
The slope is 3.
The example below shows the solution when you reverse the order of the points, calling (5, 5) Point 1 and (4, 2) Point 2.
Example
Problem
What is the slope of the line that contains the points (5, 5) and (4, 2)?
x1 = 5
y1 = 5
(5, 5) = Point 1, (x1, y1)
x2 = 4
y2 = 2
(4, 2) = Point 2, (x2, y2)
m = 3
Substitute the values into the slope formula and simplify.
Answer
The slope is 3.
Notice that regardless of which ordered pair is named Point 1 and which is named Point 2, the slope is still 3.
Advanced Example
Problem
What is the slope of the line that contains the points (3,-6.25) and (-1,8.5)?
(3,-6.25) = Point 1,
(-1,8.5) = Point 2,
Substitute the values into the slope formula and simplify.
Answer
The sl