The document discusses graphing linear equations in one variable by plotting points and identifying vertical and horizontal lines. It provides examples of writing equations to represent vertical and horizontal lines that pass through given points. Key points made include: vertical lines have the form x=a and never intersect the y-axis, horizontal lines have the form y=b and never intersect the x-axis. Homework problems ask to write equations of vertical and horizontal lines through given points.

1. Graphing Linear Equations in One Variable

2. What do each of these ordered pairs have in common? (4, -3) (4, -2) (4, -1) (4, 0) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) The x-coordinate is always the same. The y-coordinate varies. Graph each point on the same coordinate plane.

3. The equation that represents this relationship between x and y is x = 4. The graph of x = 4 is a VERTICAL LINE that crosses the x-axis at 4. All the points of this line (and no other points) have an x-coordinate of 4. y x Notice that the equation doesn’t have a y variable. The equation will never intersect the y-axis.

4. What do each of these ordered pairs have in common? (-4, -1) (-3, -1) (-2, -1) (-1, -1) (0, -1) (1, -1) (2, -1) (3, -1) (4, -1) The y-coordinate is always the same; the x-coordinate varies.

5. Notice that the equation doesn’t have an x variable. The equation will never intersect the x-axis. y The equation that represents this relationship between x and y is y = -1. The graph of y = -1 is a HORIZONTAL LINE that crosses the y-axis at -1. All the points of this line (and no other points) have y- coordinate of -1. x

6. Sketching Horizontal and Vertical Lines Sketch the graph of x = 2. y The equation does not have y as a variable. The equation says that the x-coordinate will always be 2, regardless of the value of y. x To graph the equation, put a dot on the x-axis at 2. There is no y-coordinate in the equation, so the equation of this line will never cross the y-axis.

7. Sketching Horizontal and Vertical Lines Sketch the graph of y = -3. y The equation does not have x as a variable. The equation says that the y-coordinate will always be -3, regardless of the value of x. x To graph the equation, put a dot on the y-axis at -3. There is no x-coordinate in the equation, so the equation of this line will never cross the x-axis.

8. Sketch the graphs of x = 7 and y = -4. Find the point of intersection of the two graphs. y Graph x = 7. Plot a point on the x-axis at 7. The equation has no y-value, so the line will never cross the y-axis. x Graph y = -4. Plot a point on the y-axis at -4. The equation has no x-value, so the line will never cross the x-axis. (7, -4)

9. Sketch the graphs of x = -4 and y = -1. Find the point of intersection of the two graphs. y Graph x = -4. Plot a point on the x-axis at -4. The equation has no y-value, so the line will never cross the y-axis. x Graph y = -1. Plot a point on the y-axis at -1. The equation has no x-value, so the line will never cross the x-axis. (-4, -1)

10. Write equations for the horizontal line and the vertical line that pass through the point (-7, -3) Plot the point (-7, -3). Graph a vertical line through the point. The line intersects the x-axis at -7. It never intersects the y-axis. What is its equation? y x = -7 x Graph a horizontal line through the point. The line intersects the y-axis at -3. It never intersects the x-axis. What is its equation? y = -3

11. Home work 1. Write equations for the horizontal line and the vertical line that pass through the point (-9, 4) 2. Write equations for the horizontal line and the vertical line that pass through the point (6, 7) 3. Write equations for the horizontal line and the vertical line that pass through the point (-5, 8) 4. Write equations for the horizontal line and the vertical line that pass through the point (10, -2) 5. Write equations for the horizontal line and the vertical line that pass through the point (100, -50)

12. 1. Write equations for the horizontal line and the vertical line that pass through the point (-9, 4) y x = -9 x y = 4

13. 2. Write equations for the horizontal line and the vertical line that pass through the point (6, 7) y y = 7 x = 6 x

14. 3. Write equations for the horizontal line and the vertical line that pass through the point (-5, 8) y y = 8 x = -5 x

15. 5. Write equations for the horizontal line and the vertical line that pass through the point (100, -50) 50 40 30 20 10 x -10 y = -50 -20 -30 -40 -50 -60 x = 100 -70 20 10 30 40 50 y