1.9 Patterns, Equations, and Graphs

Review: Two number lines that intersect at a right angle form a COORDINATE PLANE The horizontal axis is called the x-AXIS The vertical axis is called the y-AXIS An ORDERED PAIR of numbers names the location of a point on the plane. These numbers are the COORDINATES of the point. The first coordinate is the x-COORDINATE and the second is the y- COORDINATE The graph is split into 4 sections called: QUADRANTS

The x-y Plane: Mathematicians use a horizontal and vertical ____________ to divide a plane into four regions called ______________. axes quadrants The horizontal line is called the _____ axis. x- The vertical line is called the ____ axis. y- The x and y-axes intersect at the ___________. origin x y

The first number in an ordered pair is the ____________________. The second number in an ordered pair is the ___________________ The x-y Plane: Any point on the coordinate system is written as an ______________. ordered pair The coordinate of the origin would be represented by ________. x-coordinate y- coordinate x y

x y A B C N H V S D E F O Example 1 – Name the letter that corresponds to the following points, and give its quadrant: 1) (1, 3): ______ ______ 2) (-4, 6): ______ ______ 3) (8, -2): ______ ______ 4) (-9, -6): ______ ______ B C F A II I IV III

x y A B C N H V S D E F O Example 1 – Name the coordinates of the following points: 5) N ______ 6) H ______ 7) V ______ 8) S ______

Using Integers to Graph Equations Given a constant wind speed of 7 miles per hour, the windchill temperature can be determined by subtracting 5 from the current temperature. Basically the following is the equation for determining the windchill temperature given a 7 mph wind. _______________ = ________________ - _______________ _______________ = ______________ - ________________ or Wind Chill Actual Temperature 5 °F

Creating a table of values We can use this equation to create a table of values by substituting actual temperatures in for a to find windchill temperatures w. The two values, a and w, can be combined to form an, (a, w) Ordered Pair

Creating a table of values Actual Temp a Windchill Temp. w = a – 5 Ordered Pair (a, w)

Graphing from a Table of Values Now we can take the ordered pairs from above and graph them on a coordinate plane. The coordinate of the would be represented by. The first number in an ordered pair is the ______________ component. The second number in an ordered pair is the ____________ component. Horizontal Vertical ORIGIN (0, 0)

a w First coordinates that are negative go on the ____________of the origin. First coordinates that are positive go on the ____________of the origin. Second coordinates that are positive go ____________ the origin. Second coordinates that are negative go ____________ the origin. Left Right Below Above

Now, plot the points from the table above for (a, w).

If you connect the points, what graph would you get? _______________________ A Line The equation w = a − 5 is called a: __________ ____________ Linear Equation A linear equation is an equation whose graph is __________________. A Line

Writing Linear Equations Patterns in data can be described using linear equations. The following table gives the cost y, in dollars for renting a raft at the beach for a time x hours. Use the table to predict an equation relating the data, and predict the cost to rent a raft for 8 hours. Time (in hours), x0123 Cost (in dollars), y Equation: _______________________ Meaning: _______________________________________________ Prediction for 8 hours:____________________________ The cost of the raft rental is $10, plus $5 per hour

The solution to an equation is the set of ordered pairs that make an equation TRUE. EXAMPLE: Determine whether the given equation has the ordered pair as a solution. 1) 2) 3)

Homework : Section 1.8pages #’s 8, 12, 13, 17, 22, 24, 26, 28, 31, 34, 38, 41, 43, 55-58