Question

Which of the following describes the relationship between the lines represented by the equations 4x + 2y = 10 and y = -2x + 15?

A. They intersect and are perpendicular.
B. They coincide (represent the same line).
C. They are parallel.
D. They intersect.

Answer 1

The relationship between the lines represented by the equations 4x + 2y = 10 and y = -2x + 15 is that they are parallel. Both lines have the same slope of -2 but different y-intercepts, indicating they are parallel and will not intersect.

Step-by-step explanation:

To determine the relationship between the lines represented by the equations 4x + 2y = 10 and y = -2x + 15, we first need to look at their slopes since the slope tells us the steepness and the direction of a line.

To find the slope of the first equation, we can rearrange it into slope-intercept form (y = mx + b), where m represents the slope. For 4x + 2y = 10, we subtract 4x from both sides and then divide the entire equation by 2 to isolate y:

2y = -4x + 10
y = (-4x + 10) / 2
y = -2x + 5

So, the slope of the first line is -2. The second equation, y = -2x + 15, is already in slope-intercept form, and we can see that its slope is also -2.

Since both lines have the same slope, -2, they are parallel to each other. However, their y-intercepts are different (5 and 15, respectively), which confirms they are never going to intersect and are distinct lines. Therefore, the correct answer is that the lines are parallel.