Question

Given the graphs of f(x) = 4x - 2 and g(x) = 2x - 6, which statements are true?

A) The system has one solution.
B) The system has infinitely many solutions.
C) Any point on either line is a solution.
D) The point of intersection is the solution.
E) The point (-2, -10) is the only solution.

Answer 1

The graphs of the linear equations f(x) = 4x - 2 and g(x) = 2x - 6 intersect at a single point, making this the only solution to the system, which supports statement D) The point of intersection is the solution.

Step-by-step explanation:

When analyzing the graphs of two linear equations f(x) = 4x - 2 and g(x) = 2x - 6, we can determine the relationship between these two lines and possible solutions. Since both equations are in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can see that the slopes of the lines are different (m for f(x) is 4 and for g(x) is 2). Therefore, these two lines are not parallel and will intersect at exactly one point. This single point of intersection is the only solution to the system of equations, making statement D) The point of intersection is the solution the true statement.