Coordinate System (Parallel/Perpendicular/Intercepts)
The coordinate system is a grid system, similar to a map. Its lines are formed by two axes that are drawn perpendicular to each other. The horizontal axis is called the x-axis, and the vertical axis is called the y-axis. The two intersecting axes form four quadrants, numbered I through IV.
The point of intersection (0, 0) is called the origin. In an ordered pair, the x-coordinate is always listed first and the y-coordinate second.
The yintercept is 4
The xintercept is 6
- The graph of 2x + 3y = 12 crosses the x-axis at (6, 0), so its x-intercept is 6.
- The graph of 2x + 3y = 12 crosses the y-axis at (0, 4), so its y-intercept is 4.
Find the intercepts of the graph
y = x 5
To find the x-intercept let y = 0 and solve for x
0 = x 5
5 = x
10 = x
y = (0) 5
y = 0 5
y = 5
The x-intercept is 10, and the y-intercept is -5.
The graph of the equation contains the points (10, 0) and (0,-5). You could plot these two points and connect them to determine the graph of the line.
Compare the Slopes of Lines
Consider two different non-vertical lines 1 and 2. Line 1 has a slope, m1, and line 2 has a slope, m2. The lines are parallel if and only if they have the same slope; that would make m1 = m2.
The lines are perpendicular if their slopes are negative reciprocals of each other. Therefore, perpendicular lines have the following relationships between their slopes: