Lines in Context

Front

What does the slope represent in a linear function?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of the dependent variable when the independent variable is zero.

Front

How do you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and calculating the rise over run.

Front

What is the significance of the y-intercept in real-world contexts?

Back

The y-intercept often represents the starting value or initial condition of a situation.

Front

How do you find the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.