Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.2 Linear Functions and Their Graphs.

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Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.2 Linear Functions and Their Graphs

Linear Equation in Two Variables What did linear equation mean in Section 6.2? Ax + By = C The graph of a linear equation in two variables is a straight line.

Locating Intercepts Since a linear equation is a straight line, its graph is determined by any two distinct solutions to the equation. X-intercept, where the graph crosses the x axis Y-intercept, where the graph crosses the y axis To locate the x-intercept, set y=0 and solve the equation for x. To locate the y-intercept, set x=0 and solve the equation for y.

Example: Locating Intercepts Exercise Set 7.2 #5 Use the x and y intercepts to graph 2x + y = 6

Slope Concepts Slope provides a numerical measure for the steepness of a line. A steep line has a large slope. A horizontal line has a slope of 0. A line that goes top-left to bottom right has a negative slope. A vertical line has an undefined slope

Definition of Slope The slope of a line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is where x2 - x1 ≠ zero.

Example: Slope Exercise Set 7.2 #13 Calculate the slope of the line passing through (-2, 4) and (-1, -1). Does this line rise, fall, or is it vertical or horizontal?

Slope-Intercept Form of the Equation of a Line A linear equation of the form y = mx + b is said to be in slope-intercept form. The coefficient of x is the slope of the line (m). The constant term is its y-intercept (b).

Example: Slope-intercept Exercise Set 7.2 #25, #37 Graph the following equations using the slope and y- intercept

Horizontal Line The graph of y = b is a horizontal line. The y-intercept is b. In particular, the graph of y = 0 is the x-axis. The slope of a horizontal line is 0 Exercise Set 7.2 #43 Graph y = -2

Vertical Line The graph of x = a is a vertical line. The x-intercept is a. In particular, the graph of x = 0 is the y-axis. The slope of a vertical line is undefined. Exercise Set 7.2 #45 Graph x = 2

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.2 Linear Functions and Their Graphs