Objective:
To use points to find the slope of the line.
Vocabulary:
- Slope - The ratio of the vertical change to the horizontal change of a line.
- It describes the rate of change or slant of the line.
- Think of it as "rise over run".
- y2 - Is read 'y sub 2' and means 'y from the second point'.
- Grid Intersections - Places where the grid lines intersect.
Notes:
Slopes:
When looking at the line going from left to right (like you read):
- The slope is positive if the line goes up.
- The slope is negative if the line goes down.
- The slope is 0 (zero) if the line is horizontal.
- The slope is undefined (no slope) if the line is vertical.
Note that
zero slope and
no slope are
NOT the same thing!
- Zero slope has no rise but has run.
- No slope has rise but no run.
- No slope creates a fraction that has zero for the denominator.
- A ratio with zero for the denominator is undefined.
Slope Formula:
- y2 is the y-value from the second point.
- y1 is the y-value from the first point.
- x2 is the x-value from the second point.
- x1 is the x-value from the first point.
Hint:
An easy way to remember this is to think of skiing:
- If the slope is a positive number then you are skiing uphill.
- If it is a negative number you are skiiing downhill.
- If the slope is zero you are skiing straight across.
- If the slope is undefined it is as if you skied off of a cliff ... and now (splat) you are UNDEFINED!
Examples:
Locate two places where the line crosses grid intersections.
I see four in this graph: (−3, 6), (0, 4), (3, 2), & (6, 0).
Substitute the x and y values from two of these points into the slope formula and solve.
Be careful with the signs, this is where most mistakes are made.
It doesn't matter which two points you use. Using the last two points gives you the same answer.
Locate two places where the line crosses grid intersections.
I see five in this graph: (−4, −3), (−3, −1), (−2, 1), (−1, 3) & (0,5).
Substitute the x and y values from two of these points into the slope formula and solve.
Be careful with the signs, this is where most mistakes are made.
It doesn't matter which two points you use. Using the last two points gives you the same answer.
