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
Graph y = 2x - 1 Example
Graph y = 2x Example
Graph 2x + 3y = 4 Example
Worksheet! Time to work
Ch 7 Linear Equations
7.1 Slope
Slope Slope The ratio of the rise, or vertical change, to the run, or horizontal change rise slope = m = run
Determine the slope of each line.
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)
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?
A line contains the points whose coordinates are listed in the table. Determine the slope of the line.
Slope Formula
Determine the slope of each line. The line through the points at (3, 8) and (3, 4)
Determine the slope of each line. The line through the points at (-4, 1) and (-3, -2)
Determine the slope of each line. The line through the points at (2, 5) and (3, 9)
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, x 1, and y 1 with the values given
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
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
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
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
Write the point-slope form of an equation of the line below.
Write the point-slope form of an equation of the line below.
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)
Write an equation in slope-int form of each line with the given slope and y-int. m = 3, b = -1
Write an equation in slope-int form of each line with the given slope and y-int. m = -2/3, b = 0
Write an equation in slope-int form of each line with the given slope and y-int. m = 0, b = -4
Write an equation in slope-int form of each line with the given slope and y-int. m = 2, b = 1
Write an equation in slope-int form of each line with the given slope and y-int. m = -5/3, b = 0
Write an equation in slope-int form of each line with the given slope and y-int. m = 0, b = -8
Write an equation of the line in slopeintercept form for the situation: Slope 1 and passes through (2, 5)
Write an equation of the line in slopeintercept form for the situation: Slope -3 and passes through (1, -4)
Write an equation of the line in slopeintercept form for the situation: Passing through (-4, 4) and (2, 1)
Write an equation of the line in slopeintercept form for the situation: Passing through (6, 2) and (3, -2)
Write an equation of the line in slopeintercept form for the situation: Slope is ¾ and passes through (8, -2)
Write an equation of the line in slopeintercept 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
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.
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.
Determine whether the scatter plot shows a positive relationship, negative relationship, or no relationship. If there is a relationship, describe it.
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.
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)
Determine the x-intercept and y-intercept of the graph of the line 2y x = 8. Then graph.
Determine the x-intercept and y-intercept of the graph of the line 3x 2y = 12. Then graph.
Determine the x-intercept and y-intercept of the graph of the line x + y = 2. Then graph.
Determine the x-intercept and y-intercept of the graph of the line 3x + y = 3. Then graph.
Determine the x-intercept and y-intercept of the graph of the line 4x 5y = 20. Then graph.
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.
Determine the slope and y-intercept of the graph 6x 9y = 18.
Determine the slope and y-intercept of the graph of 4x + 3y = 6.
Graph the equation using slope intercept form. y 2 3 x 5
Graph the equation using slope intercept form. y 1 5 x 2
Graph the equation using slope intercept form. y 1 2 x 3
Graph the equation using slope intercept form. 3x y 4
Graph the equation using slope intercept form. y 3
Graph the equation using slope intercept form. x 4
Graph the equation using slope intercept form. y 1
Graph the equation using slope intercept form. x 3
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
Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs. y y 1 2 1 2 x 2 x 1
Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs. y y 5x 1 x 1
Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs. y y 2x 1 2x 5
Graph the pair of equations. Describe any similarities or differences. Explain why they are a family of graphs. y y x 1 3x 1
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?
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.
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
Determine whether the graphs of the equations are parallel. y 3x 4 9x 3y 12
Determine whether the graphs of the equations are parallel. y 2x 7 2x y
Determine whether the graphs of the equations are parallel. y 3x 3 2y 6x 5
Parallelogram A four-sided figure with two sets of parallel sides
Determine whether figure EFGH is a parallelogram.
Determine whether figure ABCD is a parallelogram.
Write an equation in slope-intercept form of 2 the line that is parallel to the graph y x 3 3 of and passes through the point at (-3, 1).
Write an equation in slope-intercept form of the line that is parallel to the graph y 6x 4 of and passes through the point at (2, 3).
Write an equation in slope-intercept form of the line that is parallel to the graph x y of and passes through the point at (2, 0). 3 2 9
Perpendicular Lines
Determine whether the graphs of the equations are perpendicular. y 2x 4 y 1 2 x 3
Determine whether the graphs of the equations are perpendicular. y y 1 x 2 5 5x 1
Determine whether the graphs of the equations are perpendicular. y 4x 3 4y x 5
y Write an equation in slope-intercept form of the line that is perpendicular to the graph of 2. x 5 and passes through the point at (2, -3).
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).
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). 2x 3y 2
Assignments #1 due today P325: 2 14 #2 due today P326: 16 38 even, 42 50