College Algebra Chapter 2 Functions and Graphs Section 2.4 Linear Equations in Two Variables and Linear Functions

1. Graph Linear Equations in Two Variables 2. Determine the Slope of a Line 3. Apply the Slope-Intercept Form of a Line 4. Compute Average Rate of Change 5. Solve Equations and Inequalities Graphically

Graph Linear Equations in Two Variables Standard form of the equation of line: Ax + By = C where A and B are real numbers and A and B are not both zero.

Example 1: Graph the equation and identify the x- and y-intercepts.

Example 2: Graph the equation and identify the x- and y-intercepts.

Example 3: Graph the equation and identify the x- and y-intercepts.

1. Graph Linear Equations in Two Variables 2. Determine the Slope of a Line 3. Apply the Slope-Intercept Form of a Line 4. Compute Average Rate of Change 5. Solve Equations and Inequalities Graphically

Determine the Slope of a Line Slope of a line through and :

Example 4: Find the slope of a line passing through the given points.

Example 5: Find the slope of a line passing through the given points.

Example 6: Find the slope of the horizontal line y = 4

Example 7: Find the slope of the vertical line x = –3

Determine the Slope of a Line Linear Equations and Slopes of Lines Ax + By = C (A  0, B  0) Slanted line y = k (k is a constant) Horizontal line x = k Vertical line Positive slope Negative Zero Undefined slope

1. Graph Linear Equations in Two Variables 2. Determine the Slope of a Line 3. Apply the Slope-Intercept Form of a Line 4. Compute Average Rate of Change 5. Solve Equations and Inequalities Graphically

Apply the Slope-Intercept Form of a Line y = mx + b slope is m, y-intercept is (0, b)

Example 8: Write the equation in slope-intercept form. Use the slope and y-intercept to graph the line.

Example 9: Write the equation in slope-intercept form. Use the slope and y-intercept to graph the line.

Example 10: Write an equation of the line in slope-intercept form that passes through the point (–2, 3) and has slope 5.

1. Graph Linear Equations in Two Variables 2. Determine the Slope of a Line 3. Apply the Slope-Intercept Form of a Line 4. Compute Average Rate of Change 5. Solve Equations and Inequalities Graphically

Compute Average Rate of Change If f is defined on the interval [x1, x2], then the average rate of change of f on the interval [x1, x2] is the slope of the secant line containing (x1, f(x1)) and (x2, f(x2)). Average rate of change: or

Examples 11 – 12: Determine the average rate of change From (–1.5, 0) to (0, 2) From (0, 2) to ( 2.5, 1)

1. Graph Linear Equations in Two Variables 2. Determine the Slope of a Line 3. Apply the Slope-Intercept Form of a Line 4. Compute Average Rate of Change 5. Solve Equations and Inequalities Graphically

Example 13: Use the graph to solve the equation.

Examples 14, 15: Use the graph to solve the inequalities.