Graphing Lines with a Table



Graphing Lines with a Table

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Example: Graph y = 2x - 1

Example: Graph y = 2x

Example: Graph 2x + 3y = 4

Ch 7 – Linear Equations

7.1 – Slope

Slope:

Example: Determine the slope of each line.

Rate of Change:

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)

The line through the points at (-4, 1) and (-3, -2)

The line through the points at (2, 5) and (3, 9)

The line through the points at (-8, 1) and (4, 1)

Types of Slope:

7.2 – Write Equations in Point-Slope Form

Point-Slope Form:

Example: Write the point-slope form of an equation for each line passing through the given point and having the given point.

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Writing from a graph:

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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.

7.3 – Writing Equations in Slope-Intercept Form

y-intercept:

x-intercept:

Slope-Intercept Form:

Example: Write an equation in slope-intercept form of each line with the given slope and y-intercept.

m = 3, b = -1

m = -2/3, b = 0

m = 0, b = -4

m = 2, b = 1

m = -5/3, b = 0

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)

Slope -3 and passes through (1, -4)

Passing through (-4, 4) and (2, 1)

Passing through (6, 2) and (3, -2)

Slope is ¾ and passes through (8, -2)

Passes through (2, 4) and (0, 5)

7.4 – Scatter Plots

Scatter Plot:

Types of Slope:

Examples: 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.

The scatter plot shows the word processing speeds of 12 students and the number of weeks they have studied word processing.

7.5 – Graphing Linear Equations

Graphing with Intercepts:

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 following equations using slope intercept form.

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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.

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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:

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

7.7 – Parallel and Perpendicular Lines

Parallel:

Parallel Lines:

Example: Determine whether the graphs of the equations are parallel.

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Parallelogram:

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 [pic] of and passes through the point at (-3, 1).

Example: Write an equation in slope-intercept form of the line that is parallel to the graph [pic] of and passes through the point at 2, 3).

Example: Write an equation in slope-intercept form of the line that is parallel to the graph [pic] of and passes through the point at (2, 0).

Perpendicular Lines:

Example: Determine whether the graphs of the equations are perpendicular.

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Example: Write an equation in slope-intercept form of the line that is perpendicular to the graph of [pic] and passes through the point at (2, -3).

Example: Write an equation in slope-intercept form of the line that is perpendicular to the graph of [pic] 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 [pic] and passes through the point at (3, 0).

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