1. Warm Up
Determine whether each equation is a linear equation. If so, write the equation in standard form and determine the x-intercept and the y-intercept.

2. Algebra 1 Glencoe McGraw-Hill JoAnn Evans
Math 8H
Graphing Linear Equations in One Variable
Algebra Glencoe McGraw-Hill JoAnn Evans

3. 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.

4. 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.

5. 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.

6. Notice that the equation doesn’t have an x variable
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 All the points of this line (and no other points) have y- coordinate of -1. x

7. 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 variable in the equation, so the equation of this line will never cross the y-axis.

8. 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 variable in the equation, so the equation of this line will never cross the x-axis.

9. Sketch the graphs of x = 7 and y = -4
Sketch the graphs of x = 7 and y = 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)

10. Sketch the graphs of x = -4 and y = -1
Sketch the graphs of x = -4 and y = 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)

11. 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