Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

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

What is the slope-intercept form of a linear equation?

Back

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

Front

If a line has a slope of 4, what does this mean?

Back

A slope of 4 means that for every 1 unit increase in x, y increases by 4 units.

Front

How do you write the equation of a line given the slope and y-intercept?

Back

Use the slope-intercept form: y = mx + b, substituting the given slope (m) and y-intercept (b).

Front

What is the cost function for a plumber charging $50 for a house call and $12 per hour?

Back

The cost function is P(x) = 50 + 12x, where x is the number of hours worked.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function and simplify.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable that makes the equation true.