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 f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the x-intercept of a linear function?

Back

To find the x-intercept of a linear function, set y (or f(x)) to 0 and solve for x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

What does it mean for y to be a function of x?

Back

For y to be a function of x, each input value (x) must correspond to exactly one output value (y). This means that no x-value can be paired with more than one y-value.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It is represented by the letter m in the linear equation.

Front

How can you determine if a table represents y as a function of x?

Back

A table represents y as a function of x if each x-value is unique and does not repeat. If any x-value corresponds to more than one y-value, it does not represent a function.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output. A relation can have multiple outputs for a single input.

Front

How do you graph a linear function given its intercepts?

Back

To graph a linear function using its intercepts, plot the x-intercept and y-intercept on the coordinate plane, then draw a straight line through these two points.

Front

What is the significance of the slope in real-world applications?

Back

The slope in real-world applications often represents a rate of change, such as speed, cost per item, or growth rate.