Why is finding the slope of a line or a curve is very important?
Why is finding the slope of a line or a curve is very important?
The concept of slope is important in maths because it is used to measure the rate at which changes are taking place.
Slope measures the rate of change in the dependent variable as the independent variable changes. The greater the slope the steeper the line.
Consider the linear function:
y = a + bx
b is the slope of the line. Slope means that a unit change in x, the independent variable will result in a change in y by the amount of b.
For instance, the slope of a line could represent velocity or acceleration, or - as in a new baby's growth chart - change in weight over time. If a graph tracks population or stock prices the slope is a measure of how quickly it is changing.
Since we can model many physical problems using curves, it is important to obtain an understanding of the slopes of curves at various points and what a slope means in real applications.
Remember: We are trying to find the rate of change of one variable compared to another.
Applications include:
- Temperature change at a particular time
- Velocity of a falling object at a particular time
- Current through a circuit at a particular time
- Variation in stockmarket prices at a particular time
- Population growth at a particular time
- Temperature increase as density increases in a gas
Hence finding slope of a line or curve is important in Physics as well as other fields.
The concept of slope is important in maths because it is used to measure the rate at which changes are taking place.
Slope measures the rate of change in the dependent variable as the independent variable changes. The greater the slope the steeper the line.
Consider the linear function:
y = a + bx
b is the slope of the line. Slope means that a unit change in x, the independent variable will result in a change in y by the amount of b.
For instance, the slope of a line could represent velocity or acceleration, or - as in a new baby's growth chart - change in weight over time. If a graph tracks population or stock prices the slope is a measure of how quickly it is changing.
Since we can model many physical problems using curves, it is important to obtain an understanding of the slopes of curves at various points and what a slope means in real applications.
Remember: We are trying to find the rate of change of one variable compared to another.
Applications include:
- Temperature change at a particular time
- Velocity of a falling object at a particular time
- Current through a circuit at a particular time
- Variation in stockmarket prices at a particular time
- Population growth at a particular time
- Temperature increase as density increases in a gas
