WELCOME TO THE MM204

UNIT 7 SEMINAR

Section 4.1: The Rectangular Coordinate System

Origin

Plot:

(2, 5)

(-3, 4)

(1, -6)

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

Section 4.1

Standard Form of an Equation Ax + By = C If a letter is missing, that means a or b must

be zero.

Examples:

2x + 3y = -7 3x – 5y = 8

a = 2 a = 3

b = 3 b = -5

c = -7 c = 8

Section 4.1

A Solution to an Equation A solution is a point on the line when

graphed. Without graphing, a solution makes the

statement true. Example: Is (-1, 1) a solution to 2x – 3y = -5?

2(-1) – 3(1) = -5 Plug in the point.

-2 – 3 = -5 Simplify.

-5 = -5 True Statement.

Yes, (-1, 1) is a solution to the equation 2x – 3y = -5

Section 4.1

Getting y alone We need to learn how to get y alone in an

equation. This will help us identify the slope.1: Get rid of fractions.2: Remove parentheses.3: Combine like terms.4: Get all the y’s on one side and everything else on the other side.5: If there’s a number in front of y, divide both sides by it.6: Simplify if necessary.

Getting Y Alone

Example: Solve 3x + 5y = 15

3x - 3x + 5y = -3x + 15 Subtract 3x from each side to get the y-term alone.

5y = -3x + 15 Simplify on each side.

Divide by 5 on both sides.

Simplify.353

515

53

5

5

xy

xy

Getting Y Alone

Solve 4x + 2(5 - y) = 6 for y.

4x + 10 - 2y = 6 Use the dist. prop. to get rid of parenths.

4x + 10 - 10 - 2y = 6 - 10 Subtract 10 from each side to get y-term alone.

4x - 2y = -4

4x - 4x - 2y = -4x - 4 Subtract 4x from each side to get y-term alone.

-2y = -4x – 4

Divide each side by -2 to get y alone.

y = 2x + 2

24

24

2

2

xy

Section 4.1

Finding Missing Coordinates Given an x or y. Plug into equation to find missing coordinate.

Example: Find the missing coordinate: 2x + 3y = 5 and (2, ?)

2(2) + 3y = 5 Plug in 2 for x.

4 + 3y = 5 Simplify.

3y = 1 Subtract 4 from each side to get y-term alone.

y = 1/3 Divide both sides by 3 to get y alone.

The point is (2, 1/3).

Section 4.2: Graphing a Linear Equation

Steps for Graphing a Linear Equation1. Determine three ordered pairs that are

solutions to the equation.2. Plot the points.3. Draw a straight line through the points.

Example: Let’s graph the equation 2x + y = 6

To determine three points, we get to pick numbers for x and/or y!

We’ll do that on the next slide.

Finding Points

Graph 2x + y = 6.

x 2x + y = 6 y (x, y)

Graphing

Plot the points:

(0, 6)

(3, 0)

(1, 4)

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

Memory Aids for Lines

HOY Horizontal lines. 0: Zero (0) slope. Y = number will be what the equation looks like.

VUX Vertical lines. Undefined slope. X = number is what the equation will look like.

Section 4.3: The Slope of a Line

Slope Tells us how the line will slant on the graph.

Formula: m =

Example: Find the slope of a line that passes through the points (2, 3) and

(5, 7).

m =

m =

12

12

xx

yy

2537

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Section 4.3

Slope – Intercept Form y = mx + b m is slope. (0, b) is the y-intercept.

Example: What is the slope and y-intercept for y = -5x + 7?

Slope is -5.

(0, 7) is the y-intercept.

Section 4.3

Parallel Lines Same Slope!

Example: Line A has a slope of 5. What is the slope of every line parallel to Line A?

Since parallel lines have the same slope, the slope must be 5.

Section 4.3

Perpendicular Lines Opposite, Reciprocal Slopes

Example: Line A has a slope of 5. What is the slope of every line perpendicular to Line A?

Since perpendicular lines have opposite, reciprocal slopes, the slope must be .

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