Linear Functions and solving equations, inequalities and absval.

Front

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

Back

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

Front

How do you convert a standard form equation to slope-intercept form?

Back

To convert a standard form equation (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, characterized by a constant rate of change.

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, indicating how steep the line is.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you determine if a function is linear or nonlinear?

Back

A function is linear if it can be expressed in the form y = mx + b. If it involves variables raised to a power other than one, it is nonlinear.

Front

What is the significance of the coefficients in the equation of a line?

Back

The coefficients in the equation of a line determine the slope and y-intercept, which define the line's steepness and position on the graph.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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 does it mean for a line to be vertical or horizontal?

Back

A vertical line has an undefined slope and is represented by an equation of the form x = a. A horizontal line has a slope of 0 and is represented by an equation of the form y = b.