Interpreting Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed 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 function represent?

Back

The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you find the y-intercept from an equation?

Back

To find the y-intercept from an equation in the form y = mx + b, set x to 0 and solve for y. The value of y will be the y-intercept.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a linear function has a slope of -1, what does this indicate about the function?

Back

A slope of -1 indicates that for every unit increase in x, y decreases by 1 unit, showing a negative relationship.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values are constant when the x-values increase by the same amount.

Front

What does the term 'rate of change' mean in the context of linear functions?

Back

Rate of change refers to how much the output (y) changes for a given change in the input (x). In linear functions, this is constant and equal to the slope.

Front

How do you write the equation of a line given two points (x1, y1) and (x2, y2)?

Back

First, calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to write the equation.

Front

What is the significance of the x-intercept in a linear function?

Back

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