y-intercepts Graph each linear equation and label the y-intercept. Write a rule to determine the y-coordinate of the y-intercept of a graph from its linear equation. Chapter 5 Discovery 1

Linear Equations in Two Variables, ax + by = c, where c = 0 Graph the following linear equations in two variables and label the x-intercept and y-intercept: Write a rule for determining when the graph of an equation has one point that is both the x-intercept and y-intercept. Chapter 5 Discovery 2

Types of Slopes Determine the slopes of the following graphs: 1. 1 of In exercises 1 and 2, the linear function is increasing. The slopes have a positive/negative value. Viewing the graphs from left to right, the graphs both rise/fall. 11. In observing the absolute value of the slope, we see that the larger the absolute value, the more/less steep is the graph. Chapter 5 Discovery 3

Types of Slopes Determine the slopes of the following graphs: 2 of In exercises 3 and 4, the linear function is decreasing. The slopes have a positive/negative value. Viewing the graphs from left to right, the graphs both rise/fall. Chapter 5 Discovery In observing the absolute value of the slope, we see that the larger the absolute value, the more/less steep is the graph.

Types of Slopes Determine the slopes of the following graphs: 3 of In exercise 5, the linear function is constant. The slope is 0/undefined. The graph is a vertical/horizontal line. 10. In exercise 6, the graph does not represent a function. The slope is 0/undefined. The graph is a vertical/horizontal line. Chapter 5 Discovery 3

Slope Formula 1. Locate and label the points ( 1, 3 ) and ( 5, 4 ) on a graph. Draw a line connecting the points. Draw the legs of a right triangle needed to determine the slope of the line, and label each length. 2. The rise of the graph is _____. 3. The run of the graph is _____. 4. The difference of the y-coordinates of the ordered pair is = _____. 5. The difference of the x-coordinates of the ordered pair is = _____. 6. The slope of the graph is _____. Write a rule to determine the slope of a graph from the coordinate of two ordered pairs. Chapter 5 Discovery 4

Determining Slope from a Linear Equation 1. Graph the given linear equations in two variables. Label two integer coordinate points. 2. Determine the slope of each of the preceding lines. 3. Determine the coefficient of the x-term in each of the equations in part 1. Write a rule to determine the slope of the graph from a linear equation in two variables. Chapter 5 Discovery 5

Chapter 5 Discovery 6 Coinciding Lines 1. Graph the given pairs of linear equations. 2. Determine the slope and y-coordinate of the y-intercept for each graph. Choose the correct answers. 3. The lines graphed are coinciding/parallel/intersecting/intersecting and perpendicular. 4. The slopes, m, in each pair of linear equations are equal/not equal. 5. The y-coordinates of the y-intercepts, b, in each pair of linear equations are equal/not equal. Write a rule for determining that the graphs of two linear equations in two variables are coinciding.

Chapter 5 Discovery 7 Parallel Lines 1. Graph the given pairs of linear equations. 2. Determine the slope and y-coordinate of the y-intercept for each graph. Choose the correct answers. 3. The lines graphed are coinciding/parallel/intersecting/intersecting and perpendicular. 4. The slopes, m, in each pair of linear equations in two variables are equal/not equal. 5. The y-coordinates of the y-intercepts, b, in each pair of linear equations in two variables are equal/not equal. Write a rule for determining that the graphs of two linear equations in two variables are parallel.

Chapter 5 Discovery 8 Intersecting Lines 1. Graph the given pairs of linear equations. 2. Determine the slope and y-coordinate of the y-intercept for each graph. Choose the correct answers. 3. The lines graphed are coinciding/parallel/intersecting/intersecting and perpendicular. 4. The slopes, m, in each pair of linear equations in two variables are equal/not equal. Write a rule for determining that the graphs of two linear equations in two variables are intersecting.

Chapter 5 Discovery 9 Perpendicular Lines 1. Graph the given pairs of linear equations. 2. Determine the slope and y-coordinate of the y-intercept for each graph. Choose the correct answers. 3. The lines graphed are coinciding/parallel/intersecting/intersecting and perpendicular. 4. The slopes, m, in each pair of linear equations in two variables are equal/not equal. 5. The two slopes, m, in each pair of linear equations in two variables are reciprocals and have the same/opposite sign. Write a rule for determining that the graphs of two linear equations in two variables are intersecting and perpendicular.