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 f(x) = 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 the y-value changes for a one-unit increase in the x-value.

Front

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

Back

The y-intercept is found by setting x = 0 in the function's equation and solving for y.

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 slope-intercept form of a linear equation?

Back

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

Front

If a linear function has a slope of -3, what does this indicate about the graph?

Back

A slope of -3 indicates that for every 1 unit increase in x, the value of y decreases by 3 units, resulting in a downward sloping line.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

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

Back

The x-intercept is the point where the graph of the function crosses the x-axis, which occurs when y = 0.

Front

Write the equation of a line with a slope of 2 that passes through the point (1, 3).

Back

The equation is y - 3 = 2(x - 1), which simplifies to y = 2x + 1.

Front

What is the graphical representation of the equation y = -x + 2?

Back

The graph is a straight line that slopes downward, crossing the y-axis at (0, 2) and the x-axis at (2, 0).