Page 481 - Algebra 1

L E S S O N Making and Analyzing Scatter Plots 71
Warm Up
New Concepts
1. Vocabulary The constant m in the __________ form y = mx + b is the
(49)
slope of the line.
2. The equation of a line is y = -2x + 6. What is the slope of the line?
(49)
3. Write the equation x - 2y = 4 in slope-intercept form.
(49) _3
4. Write an equation in slope-intercept form for a line with slope = 8 and
(49) y-intercept = -4.
One type of graph that relates two sets of data with plotted ordered pairs is called a scatter plot. Scatter plots are considered discrete graphs because their points are separate and disconnected. The points on scatter plots sometimes form a linear pattern. In these situations, a line can be drawn to model the pattern, which is called a trend line. A trend line is a line on a scatter plot, which shows the relationship between two sets of data.
Graphing a Scatter Plot and a Trend Line
Use the data in the table.
a. Make a scatter plot of the data. Then draw a trend line on the scatter plot.
SOLUTION Plot the points on a coordinate plane. Then draw a straight line as near to as many of the points as possible.
b. Find an equation for the trend line. SOLUTION Use two points on or near the trend
line t_o write an equation for the line. m= y2 -y1
Example
1
Caution
A trend line does not have to go through any of the points on the scatter plot. It has to be drawn equally as close to one point as to another so that it models the approximate slope of the points.
x
1
2
3
4
5
6
y
4
10
12
18
23
29
y
Math Reasoning
Predict Using the
table, the graph, or the equation from Example 1, what do you think would be a reasonable y-value for an x-value of 7?
Online Connection www.SaxonMathResources.com
_x - x 21
= 29 - 4 6-1
=5
(y - y1) = m(x - x1)
(y - 4) = 5(x - 1) y = 5x - 1
Find the slope of the line; use (1, 4) and (6, 29).
Write the equation for the line. Substitute m = 5 and (1, 4) for (x1, y1). Solve for y.
466 Saxon Algebra 1
40
30
20
10
x
2
4
6