Download Slope, Intercepts, and Equations of Lines

Math Models with Applications
HS Mathematics
Unit: 05 Lesson: 02
Slope, Intercepts, and Equations of Lines (pp. 1 of 5)
One specific type of relation is the ____________________. The linear parent function is ________.
Important parts of a linear function are the _________________ and ________________.
Slope – ________________________
Methods to determine slope
rise
.
ƒ From a graph, count
run
ƒ
From a table find the average
ƒ
From an equation y
'y
change in y
or
.
'x
change in x
mx b , the slope is the m value.
Intercepts – ____________________________________________
y-intercept (0, y)
ƒ From a graph determine where the line crosses the y-axis. Graph points and extend the
line if necessary.
ƒ From an equation in the form y mx b , the y-intercept is the b value.
ƒ From other equations plug in 0 for x and solve for the y value.
x-intercept (x, 0)
ƒ From a graph determine where the line crosses the x-axis. Graph points and extend the
line if necessary.
ƒ From an equation plug in 0 for y and solve for the x value.
Equations of lines
x _____________________: ax + by = c (No fractions and x is positive value)
x ____________________________: y mx b
To determine the equation of the line:
x With slope and intercept plug into y mx b .
x With a slope and point use the slope to determine a second point, and calculate a line of
regression.
x With two points calculate a line of regression.
x With a table of values calculate a line of regression.
When using two points to calculate the line of regression, the calculator will give you an r value of +1
or -1. What does this indicate?
© 2009, TESCCC
08/01/09
page 22 of 50
Math Models with Applications
HS Mathematics
Unit: 05 Lesson: 02
Slope, Intercepts, and Equations of Lines (pp. 2 of 5)
Special lines
x x = # Vertical line, undefined slope
x
y = # Horizontal line, zero slope
x
Parallel lines have equal slope.
x
Perpendicular lines have negative reciprocal slope.
Sample Problems:
1.
2.
a. Set up a table of values for at least
four points.
b. Find the slope.
c. Determine the equation of the line.
d. Identify the x- and y-intercepts.
© 2009, TESCCC
a. Set up a table of values for at least
four points.
b. Find the slope.
c. Determine the equation of the line.
d. Identify the x- and y-intercepts.
08/01/09
page 23 of 50
Math Models with Applications
HS Mathematics
Unit: 05 Lesson: 02
Slope, Intercepts, and Equations of Lines (pp. 3 of 5)
3.
x
-1
1
3
5
y
10
4
-2
-8
a. Find the slope.
b. Determine the
equation of the line.
c. Graph the function.
d. Identify the x- and yintercept.
5. y
a.
b.
c.
d.
2
x4
3
Set up a table of values.
(at least four points)
Graph the function.
Find the slope.
Identify the x- and yintercepts.
© 2009, TESCCC
4.
x
-3
-1
0
2
y
-7
-1
2
8
a. Find the slope.
b. Determine the
equation of the line.
c. Graph the function.
d. Identify the x- and yintercept.
6. y = 2x - 7
a. Set up a table of values.
(at least four points)
b. Graph the function.
c. Find the slope.
d. Identify the x- and yintercepts.
08/01/09
page 24 of 50
Math Models with Applications
HS Mathematics
Unit: 05 Lesson: 02
Slope, Intercepts, and Equations of Lines (pp. 4 of 5)
Practice Problems
1. For the function graphed above:
a. Set up a table of values. (at least four points)
b. Find the slope.
c. Determine the equation of the line.
d. Identify the x- and y-intercepts.
2. For the table below:
a. Find the slope.
b. Determine the equation of the line.
c. Graph the function.
d. Identify the x- and y-intercepts.
x
-6
-3
3
9
© 2009, TESCCC
y
3
4
6
8
08/01/09
page 25 of 50
Math Models with Applications
HS Mathematics
Unit: 05 Lesson: 02
Slope, Intercepts, and Equations of Lines (pp. 5 of 5)
3
x 5
2
Set up a table of values. (at least four points)
Graph the function.
Find the slope.
Identify the x- and y-intercepts.
3. For the equation y
a.
b.
c.
d.
Given information, find the equation of the line in y-intercept form.
4. Contains point (-1, 2) and is parallel to 4x – 2y = -3
5. Contains point (5, -3) and is perpendicular to y = 5x - 4
6. Contains (-4, 3) and is perpendicular to y = 2
7. Contains (8, -1) and is parallel to y = 1
8. Sue Ellen works at JoAnn’s Dress Shop. She is paid a salary of $280 dollars a week plus 20%
commission on her sales. Create a data table and determine a rule to represent the amount
Sue Ellen is paid as a relation of the amount of sales she makes in the week.
a. What is the rate of change? What does it represent in the problem situation?
b. What is the y-intercept? What does it represent in the problem situation?
c. What is the x-intercept? What does it represent in the problem situation?
d. If Sue Ellen sold $500 in merchandise during the week, what would be her total pay?
e. On Sue Ellen’s biggest selling week of the year, her total pay was $760. How much
merchandise did she sell that week?
© 2009, TESCCC
08/01/09
page 26 of 50