Slanting Lines
If a slanting line passes through the origin, its equation can always be written as y = mx, where m is its slope. For example, an equation of the line below is given in the graph:
Notice that the slope is 2/3 and each of the points is a solution to the equation. For example, the point (6, 4) is a solution, because 2/3 of 6 is 4.
A slanting line that does not contain the origin can be thought of as a line that has been moved up or down. For example, the following line is the previous line moved down 3 units:
When you move a point up or down, you just change the y-coordinate by adding or subtracting the distance moved. Since this applies to all points on our new line, we must subtract 3 from all the points, and therefore from the equation. So the new equation is:
Now the –3 is the y-intercept. That makes sense, since the point (0, 0) on the original line was moved down 3 units.
In general, an equation of a slanting line with slope m and y-intercept b can be written as:
y = mx + b
Another example:
The slope of this line is negative since it goes downhill from left to right, and its y-intercept is 5:
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Date last modified: October 10, 2008.