Section 3.1 Graphs of Linear Equations

OBJECTIVES Graph (plot) ordered pairs of numbers. Determine the coordinates of a point in the plane. B

OBJECTIVES Read and interpret ordered pairs on a line graph. Read and interpret ordered pairs on a bar graph. D

OBJECTIVES Find the quadrant in which a point lies. Given a chart or ordered pairs, make a line graph. F

RULES (x, y) x-coordinate y-coordinate Tells us go right or left Tells us to go up or down

(x,y) SIGNS BY QUADRANT II I (-,+) (+,+) III IV (-,-) (+,-)

Section 3.1 Exercise #1 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Section 3.1 Exercise #2 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Section 3.1 Exercise #3 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Wind Chill Temperature Comparison Wind Speed (mph) Wind chill temperature (°F) Old wind chill formula New wind chill formula

Wind Chill Temperature Comparison Wind Speed (mph) Wind chill temperature (°F) Old wind chill formula New wind chill formula

Wind Chill Temperature Comparison Wind Speed (mph) Wind chill temperature (°F) Old wind chill formula New wind chill formula

Wind Chill Temperature Comparison Wind Speed (mph) Wind chill temperature (°F) Old wind chill formula New wind chill formula

Wind Chill Temperature Comparison Wind Speed (mph) Wind chill temperature (°F) Old wind chill formula New wind chill formula

Wind Chill Temperature Comparison Wind Speed (mph) Wind chill temperature (°F) Old wind chill formula New wind chill formula

Wind Chill Temperature Comparison Wind Speed (mph) Wind chill temperature (°F) Old wind chill formula New wind chill formula

Section 3.1 Exercise #4 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Length of loan (in months) Monthly payment (in dollars)

What is the monthly payment if you want to pay off the loan in: Length of loan (in months) Monthly payment (in dollars)

What is the monthly payment if you want to pay off the loan in: Length of loan (in months) Monthly payment (in dollars)

What is the monthly payment if you want to pay off the loan in: Length of loan (in months) Monthly payment (in dollars)

Section 3.1 Exercise #5 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Determine the quadrant in which each of the points is located:

Determine the quadrant in which each of the points is located:

Determine the quadrant in which each of the points is located:

Determine the quadrant in which each of the points is located:

Section 3.1 Exercise #6 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

The ordered pairs represent the old wind chill temperature in degrees Fahrenheit when the wind speed in miles per hour is as indicated. Wind speed Wind chill Wind Speed Wind Chill

Wind speed Wind chill Wind Speed Wind Chill

Wind speed Wind chill Wind Speed Wind Chill

Wind speed Wind chill Wind Speed Wind Chill

Section 3.2 Graphs of Linear Equations

OBJECTIVES Determine whether a given ordered pair is a solution of an equation. A

OBJECTIVES Find ordered pairs that are solutions of a given equation.

OBJECTIVES Graph linear equations of the forms C

OBJECTIVES Solve applications involving linear equations. D

PROCEDURE Graphing lines Choose a value for one variable, calculate the value of the other variable, graph the resulting ordered pair.

PROCEDURE Graphing lines Repeat step 1 to obtain at least two ordered pairs.

PROCEDURE Graphing lines Graph the ordered pairs and draw a line passing through the points.

RULE Straight-Line Graphs The graph of a linear equation of the form:

Not Linear

5 –5 5 –5

5 -5 5 -5

5 -5 5 -5

Section 3.2 Exercise #7 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

No

Section 3.2 Exercise #8 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

In (x, 2), y = 2 so 3x – y = 10 becomes: 3x – 2 = 10 add 2: 3x = 12 divide by 3: x = 4

Section 3.2 Exercise #9 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Section 3.2 Exercise #10 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Section 3.2 Exercise #11 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Section 3.3 Graphs of Linear Equations

OBJECTIVES Graph lines using intercepts. A

OBJECTIVES Graph lines passing through the origin. B

OBJECTIVES Graph horizontal and vertical lines. C

OBJECTIVES Solve applications involving graphs of lines. D

PROCEDURE x- and y- intercepts The x-intercept (a, 0) is the point at which the line crosses the x-axis. To find the x-intercept, let y = 0 and solve for x.

PROCEDURE x- and y- intercepts The y-intercept (0, b) is the point at which the line crosses the y-axis. To find the y-intercept, let x = 0 and solve for y.

PROCEDURE Graph a Line Using Intercepts Find the x-intercept (a, 0) Find the y-intercept (0, b)

PROCEDURE Graph a Line Using Intercepts Graph (a, 0) and (0, b), then connect them with a line. Find a third point to use as a check.

PROCEDURE Graphing Lines Through the Origin. Use the point (0, 0), and another point, then draw the line passing through both. Verify with a third point.

NOTE y = k is a horizontal line crossing the y-axis at k.

NOTE x = k is a vertical line crossing the x-axis at k.

Section 3.3 Exercise #12 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Section 3.3 Exercise #13 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Section 3.3 Exercise #14 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Vertical line

Section 3.3 Exercise #15 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Horizontal line

Section 3.4 Graphs of Linear Equations

OBJECTIVES Find the slope of a line given two points. A

OBJECTIVES Find the slope of a line given the equation of the line. B

OBJECTIVES Determine whether two lines are parallel, perpendicular, or neither. C

OBJECTIVES Solve an application. D

DEFINITION SLOPE

DEFINITION SLOPE

NOTE SLOPE OF y = mx + b The slope of the line defined by the equation y = mx + b is m.

PROCEDURE Finding a Slope. Solve the equation for y. The slope is m, the coefficient of x.

DEFINITION Slopes of Parallel and Perpendicular Lines Two lines with the same slope but different y-intercepts are parallel.

DEFINITION Slopes of Parallel and Perpendicular Lines Two lines whose slopes have a product of –1 are perpendicular.

Section 3.4 Exercise #16 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Find the slope of the line going through:

Find the slope of the line going through:

Find the slope of the line going through:

Section 3.4 Exercise #17 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Find the slope of the line going through:

Find the slope of the line going through: Undefined

Find the slope of the line going through:

Section 3.4 Exercise #18 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

slope

Section 3.4 Exercise #19 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

Decide whether the lines are parallel, perpendicular or neither.

Decide whether the lines are parallel, perpendicular or neither.

Decide whether the lines are parallel, perpendicular or neither.

Decide whether the lines are parallel, perpendicular or neither. and

Section 3.4 Exercise #20 Chapter 3 Graphs of Linear Equations Let’s work Exercise #19 from Section 5.1

The number N of stores in a city t years after 2000 can be approximated by Annual increase in the number of stores