GOAL: To understand and graph linear equations of one variable
Study the following points:
(4,-2) , (4,-1) , (4,0) , (4,1) , (4,2) , (4,3)
The y-coordinates here vary while the x-coordinates are always 4.
The equation that represents this relationship between x and y is x=4.
Similarly, we can graph horizontal lines:
Study the following points:
(-2,1) , (-1,1) , (0,1) , (1,1) , (2,1) , (3,1)
The x-coordinates here vary while the y-coordinates are always 1.
The equation that represents this relationship between x and y is y=1.
In the coordinate plane, the graph of y=1 is the horizontal line that crosses the y-axis at 1 because all the points of this line, and no other points, have y-coordinate 1.
1. In the coordinate plane, the graph of x=a is a vertical line where a is any real number.
2. In the coordinate plane, the graph of y=b is a horizontal line where b is any real number.
x-coordinate must be a.
y-coordinate can have any value.
x-coordinate can have any value.
y-coordinate must be b.
The point of intersection of a horizontal line and a vertical line must have an x-coordinate of a, and a y-coordinate of b.
Intersection Point: (a,b)
Show the graphs of x=5 and y=7 on the same axis. Find the point of intersection.
X-axis is the line y=0. (The horizontal line with y-coordinate 0)
Y-axis is the line x=0. (The vertical line with x-coordinate 0)
The intersection point of the X-axis and Y-axis is the origin, the point with coordinates (0,0)