Graphing Linear Equations Section 1.2

Lehmann, Intermediate Algebra, 3ed Section 1.2 Consider the equation. Let’s find y when So, when, which can be represented by the ordered pair Slide 2 Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 For an ordered pair, we write the value of the independent variable in the first (left) position and the value of the dependent variable in the second (right) position. The numbers a and b are called coordinates. For the x-coordinate is 3 and the y-coordinate is 1. Slide 3 Definition of Solution, Satisfy, and Solution Set Definition Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 The equation becomes a true statement when we substitute 3 for x- coordinate and 1 for y-coordinate. Slide 4 Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 An ordered pair is a solution of an equation in terms of x and y if the equation becomes a true statement when a is substituted for x and b is substituted for y. We say satisfies the equation. The solution set of the equation is the set of all solution of the equation. Slide 5 Definition of Solution, Satisfy, and Solution Set Definition Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 Find five solutions to the equation and plot them in the coordinate system (on the right). Slide 6 Graphing an Equation Example Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 We begin be arbitrarily choosing the values 0, 1, and 2 to substitute for x: The ordered pairs and are also solutions. Slide 7 Graphing an Equation Solution Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 Create a table of solutions xy Slide 8 Graphing an Equation Plot the solutions Points form a linear line. Solution Continued Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 Every point on the line is a solution to the equation Slide 9 Graphing an Equation Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 The point lies on the line Should satisfy the equations Whereas is not on the line Thus should not satisfy the equation Slide 10 Graphing an Equation Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2Slide 11 Graphing an Equation The is not a solution to the equation Definition of Solution, Satisfy, and Solution Set

Lehmann, Intermediate Algebra, 3ed Section 1.2 Sometimes we find intercepts to graph a line. x-intercept is on the y-axis, so y = 0 y-intercepts in on the x-axis, so x = 0 Slide 12 Property For an equation containing the variables x and y x-intercept: Substitute y = 0 and solve for x y-intercept: Substitute x = 0 and solve for y Directions Finding Intercepts of a Graph

Lehmann, Intermediate Algebra, 3ed Section 1.2 Use intercepts to sketch a graph of Slide 13 Using Intercepts to Sketch a Graph x-intercept: Set y = 0. Example Solution Finding Intercepts of a Graph

Lehmann, Intermediate Algebra, 3ed Section 1.2 y-intercept: Set x = 0. So, the x-intercept is and y-intercept is Slide 14 Using Intercepts to Sketch a Graph Solution Continued Finding Intercepts of a Graph

Lehmann, Intermediate Algebra, 3ed Section 1.2 Graph the equation of Slide 15 Graphing a Vertical Line xy Notice that the values of x must be 3, but y can have any value. Some solutions are listed to the left. Example Solution Finding Intercepts of a Graph

Lehmann, Intermediate Algebra, 3ed Section 1.2 Graph the equation of Slide 16 Graphing a Horizontal Line x y –2 –5 –1 –5 0 –5 1 –5 2 –5 Notice that the values of y must be –5, but x can have any value. Some solutions are listed to the left. Example Solution Vertical and Horizontal Lines

Lehmann, Intermediate Algebra, 3ed Section 1.2 If a and b are constants: An equation that can be put into the form. has a vertical line as its graph An equation that can be put into the form.has a horizontal line as its graph Slide 17 Vertical and Horizontal Line Property Property Vertical and Horizontal Lines