# On The Real Number Line and on Cartesian Coordinates Presented by: Vicki Angel and Jan Whisonant Transitions Math Conference Austin, TX May 6-7, 2011.

## Presentation on theme: "On The Real Number Line and on Cartesian Coordinates Presented by: Vicki Angel and Jan Whisonant Transitions Math Conference Austin, TX May 6-7, 2011."— Presentation transcript:

on The Real Number Line and on Cartesian Coordinates Presented by: Vicki Angel and Jan Whisonant Transitions Math Conference Austin, TX May 6-7, 2011

OBJECTIVE The participants will learn strategies for teaching graphing of equations and inequalities in one and two variables. Points, intervals, lines, and parabolas will be included.

For each real number there corresponds exactly one point on the real number line and for each point on the real number line there corresponds exactly one real number.

Solution to an equation in one unknown

Solution to an inequality in one unknown

Solution of a compound inequality

Standard Form ax + by + c = 0 Slope- Intercept Form y = mx + b m = slope b = y intercept

y = - 4x + 8 If x = 0, then y = 8 y = -4(0) + 8 y = 0 + 8 = 8 If y = 0, then x = 2 0 = - 4x + 8 4x = 8, x = 2

y = 5/4 x – 2 y intercept = - 2 slope = 5/4

y = 3/2 x + 3 x y 0 3 2 6 - 4 - 3

 Select a point that is not on the line.  Substitute the x and y values of the point into the inequality.  If those values make the inequality true, then shade the side of the line that the point is on.  If those values make the inequality false, then shade the opposite side of the line from the selected point.

y intercept = 2 slope = - 8/3

y intercept = 4 slope = 6/1

Find the vertex and at least two other points on the graph, then use the axis of symmetry to add two more points to the graph. When the equation is in the form The vertex is (h, k) and the line of symmetry is x = h

x y 0 0 2 4 - 3 9

Vertex (3,4) Line of symmetry: x=3 x y 4 1 2 - 4

Vertex: (1, -5) Line of symmetry: x=1 7 -2 3 0 xy

x - 4 1 y - 1 1 6 - 2 y ≥ (x+2)² - 3

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