Understanding Linear Functions

What is the definition of a linear function?

• A linear function is a function of the form f(x) = mx + b, where m and b are constants.

• A linear function is a function that has a variable exponent.

• A linear function is defined as f(x) = ax^2 + bx + c, where a, b, and c are constants.

• A linear function is a function that curves in a parabolic shape.

Identify the slope of the line represented by the equation y = 3x + 2.

• 5

• 3

• 1

• -3

Graph the linear function y = -2x + 5 on a coordinate plane.

• Graph the line passing through points (0, 5) and (2, 1).

• Graph the line passing through points (1, 5) and (2, 3).

• Graph the line passing through points (0, 0) and (1, 1).

• Graph the line passing through points (0, 5) and (1, 3).

What does the slope of a line represent in a linear function?

• The slope indicates the y-intercept of the line.

• The slope shows the maximum value of the function.

• The slope represents the distance between two points on the line.

• The slope represents the rate of change of the function.

If a line has a slope of 0, what can you say about its graph?

• The graph of the line is diagonal.

• The graph of the line is curved.

• The graph of the line is vertical.

• The graph of the line is horizontal.

Determine the slope of the line that passes through the points (1, 2) and (3, 6).

• 1

• 2

• 3

• 0

What is the y-intercept of the function y = 4x - 1?

• -4

• 1

• 0

• -1

How do you convert the equation of a line from standard form to slope-intercept form?

• y = Ax + B

• y = (B/A)x + C

• y = (C/A)x + B

• y = (-A/B)x + (C/B)

If the slope of a line is negative, what does that indicate about the direction of the line?

• The line moves vertically downward.

• The line moves downward from left to right.

• The line is horizontal and does not change direction.

• The line moves upward from left to right.

Explain how to find the x-intercept of a linear function.

• Use the quadratic formula to find x.

• Set y = 0 and solve for x.

• Graph the function and find the intersection with the y-axis.

• Set x = 0 and solve for y.