Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you find the initial value in a linear equation?

Back

The initial value is the y-intercept (b) in the equation y = mx + b. It represents the starting value of y when x is 0.

Front

If a linear equation has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Front

What is the unit rate?

Back

The unit rate is a comparison of two different quantities when they are combined together. It is often expressed as a quantity per 1 unit of another quantity.

Front

How do you calculate the unit rate from a given total?

Back

To calculate the unit rate, divide the total amount by the number of units. For example, if you earn $200 for 8 hours of work, the unit rate is $200 ÷ 8 = $25 per hour.

Front

What is the formula for calculating the rate of change?

Back

The rate of change can be calculated using the formula: (change in y) / (change in x). It shows how much y changes for a given change in x.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as x increases, y decreases. The line slopes downward from left to right.

Front

What is the significance of the initial value in real-world problems?

Back

The initial value often represents a starting point or baseline in real-world scenarios, such as the starting amount of money or the initial population.