Finding the Slope of a Line Given Two Points (3.9.2) Flashcards
• Slope is the change from one point to another on a line. It is stated as a ratio (fraction) with change vertically over change horizontally. This is frequently referred to as rise/run.
• Slope is the change from one point to another on a line. It is stated as a ratio (fraction) with change vertically over change horizontally. This is frequently referred to as rise/run.
• Slope is the measure of pitch or steepness of a line. The larger the slope the steeper the line. A vertical line is so steep that the sideways change cannot be measured and its slope is undefined.
• Slope is the measure of pitch or steepness of a line. The larger the slope the steeper the line. A vertical line is so steep that the sideways change cannot be measured and its slope is undefined.
In the slope formula, the x1, y1, x2 and y2 values come from two points on the line, (x1, y1) and (x2, y2). It does not matter which of two points is chosen to be (x1, y1) and which is chosen to be (x2, y2). Therefore, the slope of a line may also be calculated by subtracting y1 – y2 and dividing that by x1 – x2.
In the slope formula, the x1, y1, x2 and y2 values come from two points on the line, (x1, y1) and (x2, y2). It does not matter which of two points is chosen to be (x1, y1) and which is chosen to be (x2, y2). Therefore, the slope of a line may also be calculated by subtracting y1 – y2 and dividing that by x1 – x2.
In this example, we find the change between the two points by doing three things:
- Subtract the two y-values, 5 and 1, and
write that as the numerator of our ratio. - Subtract the two x-values, 5 and 1, and
write that as the denominator of our ratio. - Reduce the fraction if possible.
The slope is 1 which tells us that the graph is rising at the
same rate it is moving sideways.
In this example, we follow the same process.
Remember: Decide which point is (x2,y2) and be sure to
use its coordinates first on both levels. If you don’t, your
signs will be incorrect.
In this case, we have –7 –0 = –7 over –3 –2 = –5. So, our
slope is 7/5. This tells us that the graph is moving up 7 units for each 5 units it moves to the right. Note: A positive slope indicates a line that is climbing when viewed from left to right. Note: A negative slope indicates a line that is falling when viewed from left to right.
In this example, we find the change between the two points by doing three things:
- Subtract the two y-values, 5 and 1, and
write that as the numerator of our ratio. - Subtract the two x-values, 5 and 1, and
write that as the denominator of our ratio. - Reduce the fraction if possible.
The slope is 1 which tells us that the graph is rising at the
same rate it is moving sideways.
In this example, we follow the same process.
Remember: Decide which point is (x2,y2) and be sure to
use its coordinates first on both levels. If you don’t, your
signs will be incorrect.
In this case, we have –7 –0 = –7 over –3 –2 = –5. So, our
slope is 7/5. This tells us that the graph is moving up 7 units for each 5 units it moves to the right. Note: A positive slope indicates a line that is climbing when viewed from left to right. Note: A negative slope indicates a line that is falling when viewed from left to right.
