Question

Which of the following inequalities matches the graph?

A.) −6x + y < 3
B.) 6x + y < 3
C.) 6x − y < −3
D.) The correct inequality is not listed

Answer 1

All the provided equations, A, B, and C, are linear because they can be rewritten in the standard form y = mx + b, where m represents the slope and b represents the y-intercept. Therefore, the correct answer is D, which states that both A and B are linear equations.

Step-by-step explanation:

Identifying Linear Equations

When working with linear equations, a key characteristic is that they can be written in the form y = mx + b, where m is the slope and b is the y-intercept. Looking at the provided options, let's determine which equations are linear:

• A. y = -3x: This equation is linear with a slope of -3 and a y-intercept of 0.
• B. y = 0.2 + 0.74x: This is also a linear equation with a slope of 0.74 and a y-intercept of 0.2.
• C. y = -9.4 - 2x: While this appears to have constants and a variable x, it can be rewritten as y = -2x - 9.4, which shows it is a linear equation with a slope of -2 and a y-intercept of -9.4.

Now we can see all the options presented are, in fact, linear equations. Option D, which mentions both A and B is the correct answer because both A and B are linear equations with different slopes and y-intercepts.