Graphing Lines with a Table - Rock Creek Schools · Graphing Lines with a Table • Select (or use...
Transcript of Graphing Lines with a Table - Rock Creek Schools · Graphing Lines with a Table • Select (or use...
Graphing Lines with a Table
• Select (or use pre-selected) values for x
• Substitute those x values in the equation and solve for y
• Graph the x and y values as ordered pairs
• Connect points with a line
Example
• Graph y = 2x - 1
Example
• Graph y = 2x
Example
• Graph 2x + 3y = 4
Time to work
• Worksheet!
Ch 7
Linear Equations
7.1
Slope
Slope
• Slope – The ratio of the rise, or vertical change, to the run,
or horizontal change
riseslope = m = run
Example
• Determine the slope of each line.
Example
• Determine the slope of each line.
Rate of Change
• In real-life applications, slope is the rate of change (how much a value is changing)
Example
• The graph below shows the distance traveled by Rebecca and Ian during a day-long bicycle ride. Find the slope of each line. To what does the slope refer?
Example
• A line contains the points whose coordinates are listed in the table. Determine the slope of the line.
Slope Formula
Example
• Determine the slope of each line. The line through the points at (3, 8) and (3, 4)
Example
• Determine the slope of each line. The line through the points at (-4, 1) and
(-3, -2)
Example
• Determine the slope of each line. The line through the points at (2, 5) and (3, 9)
Example
• Determine the slope of each line. The line through the points at (-8, 1) and (4, 1)
Types of Slope
Assignments
• #1 – due today– P287: 1, 2, 4 – 12 even
• #2 – due next time– P288: 13 – 27, 34, 35, 36
7.2
Writing Equations in Point-Slope Form
Point-Slope Form
• Replace the m, x1, and y1 with the values given
Example
• Write the point-slope form of the equation of the line passing through the given point and having the given slope.
(-2, 7), m = -1/3
Example
• Write the point-slope form of the equation of the line passing through the given point and having the given slope.
(4, 0), m = 4
Example
• Write the point-slope form of the equation of the line passing through the given point and having the given slope.
(-3, 2), m = 2
Example
• Write the point-slope form of the equation of the line passing through the given point and having the given slope.
(5, 4), m = -2/3
Writing from a graph
• You can also write an equation in point-slope form from a graph
• First find the slope of the line by counting
• Then pick a point (any point on the line will work)
• Plug those values into the formula
Example
• Write the point-slope form of an equation of the line below.
Example
• Write the point-slope form of an equation of the line below.
Example
• Write the point-slope form of an equation for the line passing through (1, 4) and (3, -5) Hints: find the slope first / it doesn’t matter which
point you use.
Assignments
• #1 – due today P293: 3 – 13
• #2 – due next time P293: 15 – 37
7.3
Writing Equations in Slope-Intercept Form
Intercepts
• y-intercept – The point on the y-axis where the line crosses that
axis
• x-intercept – The point on the x-axis where the line crosses that
axis
Slope-Intercept Form
• Another form, besides point-slope
• This form helps you graph!
y = mx + b
• m – slope
• b – y-intercept (point where it crosses y-axis)
Example
• Write an equation in slope-int form of each line with the given slope and y-int.
m = 3, b = -1
Example
• Write an equation in slope-int form of each line with the given slope and y-int.
m = -2/3, b = 0
Example
• Write an equation in slope-int form of each line with the given slope and y-int.
m = 0, b = -4
Example
• Write an equation in slope-int form of each line with the given slope and y-int.
m = 2, b = 1
Example
• Write an equation in slope-int form of each line with the given slope and y-int.
m = -5/3, b = 0
Example
• Write an equation in slope-int form of each line with the given slope and y-int.
m = 0, b = -8
Example
• Write an equation of the line in slope-intercept form for the situation:
Slope 1 and passes through (2, 5)
Example
• Write an equation of the line in slope-intercept form for the situation:
Slope -3 and passes through (1, -4)
Example
• Write an equation of the line in slope-intercept form for the situation:
Passing through (-4, 4) and (2, 1)
Example
• Write an equation of the line in slope-intercept form for the situation:
Passing through (6, 2) and (3, -2)
Example
• Write an equation of the line in slope-intercept form for the situation:
Slope is ¾ and passes through (8, -2)
Example
• Write an equation of the line in slope-intercept form for the situation:
Passes through (2, 4) and (0, 5)
Assignments
• #1 – due today P299: 4 – 12
• #2 – due next time P299: 14 – 40 even, 41 – 45, 49 – 50, 53 – 57
7.4
Scatter Plots
Scatter Plots
• Scatter Plot – Graph where two sets of data are plotted as
ordered pairs on the same coordinate plane
Used to see if there is a trend, pattern, or relationship among the variables
Scatter Plots
Example
• Determine whether the scatter plot shows a positive relationship, negative relationship, or no relationship. If there is a relationship, describe it.
• The scatter plot shows the number of years of experience and the salary for each employee in a small company.
Example• Determine whether the
scatter plot shows a positive relationship, negative relationship, or no relationship. If there is a relationship, describe it.
• The scatter plot shows the word processing speeds of 12 students and the number of weeks they have studied word processing.
Example
• Determine whether the scatter plot shows a positive relationship, negative relationship, or no relationship. If there is a relationship, describe it.
Example
• The table shows the average number of minutes a pediatric dentist spends during each appointment instructing the patient in proper dental care, and the number of cavities for each patient.
Example
• Make a scatter plot of the data. Let the horizontal axis represent instruction time and let the vertical axis represent the number of cavities.
• Does the scatter plot show a relationship between instruction time and cavities? Explain.
• Describe the independent and dependent variables. Then state the domain and the range.
Assignments
• P305: 4 – 8, 10 – 17, 19 – 23
7.5
Graphing Linear Equations
Graphing with Intercepts
• What are intercepts?– Point where the line crosses the x- and y-axes
•Find the intercepts and plot them, draw a line between•Point of y-intercept is always (o, y)•Point of x-intercept is always (x, 0)
Example
• Determine the x-intercept and y-intercept of the graph of the line 2y – x = 8. Then graph.
Example
• Determine the x-intercept and y-intercept of the graph of the line 3x – 2y = 12. Then graph.
Example
• Determine the x-intercept and y-intercept of the graph of the line x + y = 2. Then graph.
Example
• Determine the x-intercept and y-intercept of the graph of the line 3x + y = 3. Then graph.
Example
• Determine the x-intercept and y-intercept of the graph of the line 4x – 5y = 20. Then graph.
Example
• Suppose to ship a package it costs $2.05 for the first pound and $1.55 for each additional pound. This can be represented by y = 2.05 + 1.55x. Determine the slope and y-intercept of the graph of the equation.
Example
• Determine the slope and y-intercept of the graph 6x – 9y = 18.
Example
• Determine the slope and y-intercept of the graph of 4x + 3y = 6.
Example
• Graph the equation using slope intercept form.
2 53
y x
Example
• Graph the equation using slope intercept form.
1 25
y x
Example
• Graph the equation using slope intercept form.
1 32
y x
Example
• Graph the equation using slope intercept form.
3 4x y
Example
• Graph the equation using slope intercept form.
3y
Example
• Graph the equation using slope intercept form.
4x
Example
• Graph the equation using slope intercept form.
1y
Example
• Graph the equation using slope intercept form.
3x
Assignments
• P314: 7 – 11, 24 – 34 even, 36 – 38, 43 – 49
7.6
Families of Linear Graphs
Review
• Slope formula:
• Point-Slope Form:
• Slope-Intercept Form:
Linear Graphs
Example
• Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs.
1 221 12
y x
y x
Example
• Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs.
5 11
y xy x
Example
• Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs.
2 12 5
y xy x
Example
• Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs.
13 1
y xy x
Example
• Gretchen and Max each have a savings account and plan to save $20 per month. The current balance in Gretchen’s account is $150 and the balance in Max’s account is $100. Then y = 20x + 150 and y = 20x + 100 represent how much money each has in their account, respectively, after x months. Compare and contrast the graphs of the equations.
Parent Graphs
• The simplest of graphs in a family
• Questions: How does changing the slope affect the line?
How does changing the y-int affect the line?
Example
• Change y = -3x – 1 so that the graph of the new equation fits each description. Same y-intercept, less steep positive slope.
Same slope, y-intercept is shifted down 2 units.
Example
• Change y = 2x + 1 so that the graph of the new equation fits each description.– Same slope, shifted down 1 unit
– Same y-intercept, less steep positive slope
Assignments
• #1 – due today P319: 1, 4 – 10 even
• #2 – due next time P319: 12 – 30 even, 31, 34 – 39
7.7
Parallel and Perpendicular Lines
Parallel
• Two lines are parallel if they never intersect
• What would have to be true about the lines so that they would never intersect?
• They have the same slope!!
Parallel Lines
Example
• Determine whether the graphs of the equations are parallel.
3 49 3 12y xx y
Example
• Determine whether the graphs of the equations are parallel.
27 2y x
x y
Example
• Determine whether the graphs of the equations are parallel.
3 32 6 5y x
y x
Parallelogram
• A four-sided figure with two sets of parallel sides
Example
• Determine whether figure EFGH is a parallelogram.
Example
• Determine whether figure ABCD is a parallelogram.
Example
• Write an equation in slope-intercept form of the line that is parallel to the graph of and passes through the point at (-3, 1).
2 33
y x
Example
• Write an equation in slope-intercept form of the line that is parallel to the graph of and passes through the point at (2, 3).
6 4y x
Example
• Write an equation in slope-intercept form of the line that is parallel to the graph of and passes through the point at (2, 0).
3 2 9x y
Perpendicular Lines
Example
• Determine whether the graphs of the equations are perpendicular.
2 41 32
y x
y x
Example
• Determine whether the graphs of the equations are perpendicular.
1 255 1
y x
y x
Example
• Determine whether the graphs of the equations are perpendicular.
4 34 5y x
y x
Example
• Write an equation in slope-intercept form of the line that is perpendicular to the graph of . and passes through the point at (2, -3).2 5y x
Example
• Write an equation in slope-intercept form of the line that is perpendicular to the graph of and passes through the point at (0, 0).
Example
• Write an equation in slope-intercept form of the line that is perpendicular to the graph of . and passes through the point at (3, 0).2 3 2x y
Assignments
• #1 – due today P325: 2 – 14
• #2 – due today P326: 16 – 38 even, 42 – 50