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 steep the line is and the direction it goes (positive slope means the line rises, negative slope means it falls).

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

How do you find the slope between 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 of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the slope-intercept form y = mx + b.

Front

What does it mean if a line has an undefined slope?

Back

A line with an undefined slope is vertical, meaning it goes straight up and down. It cannot be expressed in the slope-intercept form.

Front

What is the equation of a line with a slope of -1 that passes through the point (2, 3)?

Back

The equation is y = -1(x - 2) + 3, which simplifies to y = -x + 5.

Front

How do you convert the equation y = -1/3x + 3 to standard form?

Back

To convert to standard form, rearrange to 1/3x + y = 3, or multiply through by 3 to get x + 3y = 9.

Front

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

Back

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

What is the significance of the coordinates (0, b) in a linear function?

Back

The coordinates (0, b) represent the y-intercept of the line, where the line crosses the y-axis.