Question

Which of the following statements are correct? Select three that apply.

A. The function y = 10x is not linear.
B. The function y = -5x - 15 is linear.
C. The function y = 2x² + 10 is not linear.
D. The graph of the function y = 12x + 1 is a straight line.
E. The graph of the function y = –20x is not a straight line.
F. The graph of the function y = 7x² + 10 is a straight line.

Answer 1

B. The function y = -5x - 15 is linear.

D. The graph of the function y = 12x + 1 is a straight line.

E. The graph of the function y = –20x is not a straight line.

Step-by-step explanation:

A. The function y = 10x is linear because it is of the form y = mx, where m is the slope.

B. The function y = -5x - 15 is linear because it is of the form y = mx + b, where m is the slope and b is the y-intercept.

C. The function y = 2x² + 10 is not linear because it contains a squared term (x²), making it a quadratic function.

D. The function y = 12x + 1 is linear because it is of the form y = mx + b.

E. The function y = -20x is linear because it is of the form y = mx, but its graph is a straight line passing through the origin (0,0).

F. The function y = 7x² + 10 is not linear because it contains a squared term (x²), making it a quadratic function.

Answer 2

The correct statements identifying linear functions and their corresponding graphs are B (y = -5x - 15), C (y = 2x² + 10 is not linear), and D (y = 12x + 1 has a straight-line graph).

Step-by-step explanation:

To determine which statements are correct regarding whether a function is linear or not, and the shape of the graphs, let's review the characteristics of a linear equation. A linear equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation is always a straight line.

Now, let's examine each statement:

• A: The function y = 10x lacks the y-intercept term, but it can be written as y = 10x + 0, thus it is, in fact, a linear equation with a slope of 10 and a y-intercept of 0. This statement is incorrect.
• B: The function y = -5x - 15 fits the form y = mx + b with m = -5 and b = -15. This is a linear equation, and its graph is a straight line. This statement is correct.
• C: The function y = 2x² + 10 includes a quadratic term (x²), so it is not linear, and its graph is not a straight line. This statement is correct.
• D: The function y = 12x + 1 is in the form y = mx + b with m = 12 and b = 1, making it a linear equation, and its graph will indeed be a straight line. This statement is correct.
• E: The function y = –20x is also linear since it can be written as y = -20x + 0. Its graph is a straight line with a negative slope. This statement is incorrect.
• F: The function y = 7x² + 10 includes a quadratic term (x²), indicating that it is not linear, so its graph will not be a straight line. This statement is incorrect.

The correct statements are B, C, and D.