Math Review: Algebra (Graph Numbers)
Slope and y-intercept | Hints: Finding the Equation of a Line Hints | Problems: Finding the Equation of a Line
Slope and y-intercept
Slope
The slope of line can tell us a lot about its steepness and direction. The slope-intercept form of an equation of a line is y=mx+b
where m is the slope.
The slope can tell us the direction in which the line slants.
- m is positive « the line slants to the left (rises)
- m is negative « the line slants to the right (falls)
y=-2x
y=2x
The slope can give us an idea of the steepness of the line.
- The larger the absolute value of m, the steeper the line.
y=3x
y=1/3x
ex: If we consider the equation of a line
the slope of -1/4 tells us that the line falls from left to right and is not very steep.
y-intercept
In the equation y=mx+b, b represents the y-coordinate of the y-intercept. The y-intercept is the point where the line intersects the y-axis.
ex. In the equation of a line y=3x+1, we can determine that this line intersects the
y-axis at (0,1).
In conclusion, if a line is written in slope-intercept form, y=mx+b, we can tell a lot about the line just by looking at the equation.
ex. Consider the equation of a line y=8x-3 which can also be written as y=8x+(-3).
From inspecting the equation, we can tell that
- The line is steep. (the absolute value of 8 is large)
- The line rises from left to right. (8 is positive)
- The line intersects the y-axis at (0,-3).
©2002, Last Updated:
June 15, 2007
El Centro College
Communications, Mathematics, Developmental Studies, and Teacher Preparation Division