Question

What is the relationship between the graphs of y = 2x and y = 2-x?

Answer 1

Both of these are linear equations with different y-intercepts and different slopes.

Let's analyze the lines:

y = 2x:

This is a linear equation with a slope of 2 and a y-intercept at the origin (0,0). This means that for every unit increase in x, y increases by 2. The graph is a straight line that passes through the origin.

y = 2 - x:

This is also a linear equation, but with a slope of -1 and a y-intercept at (0,2). This means that for every unit increase in x, y decreases by 1. The graph is a straight line that intersects the y-axis at the point (0,2).

Now, let's consider their relationship:

Both equations are linear, so their graphs are straight lines.

• The slope of the first line (y = 2x) is positive (2), indicating a upward-sloping line.
• The slope of the second line (y = 2 - x) is negative (-1), indicating a downward-sloping line.

Therefore, the graphs of these two equations are lines with different slopes. The line represented by y = 2x slopes upwards, while the line represented by y = 2 - x slopes downwards.

Answer 2

The relationship between the graphs is the intersection point at (0.667,1.333)

Explanation:

we have

y=2x ----> equation A

The slope of the line A is equal to m=2

The line passes through the origin

y=2-x ----> equation B

The slope of the line B is m=-1

The x-intercept is the point (2,0)

The y-intercept is the point (0,2)

Line A and Line B are not parallel (the slopes are not equal)

Line A and Line B are not perpendicular (the product of their slopes is not equal to -1)

so

The relationship between Line A and Line B is the intersection point both graphs

using a graphing tool

The intersection point is (0.667,1.333)

see the attached figure

The intersection point is a common point , therefore belongs to both lines