Which graph represents the following relationship between x and y?
y = 3x
The graph representing the relationship y = 3x is a straight line that passes through the origin (0,0) and has a slope of 3.
The graph that represents the relationship y = 3x is a straight line that passes through the origin (0,0) on the coordinate plane and has a slope of 3. The line rises as x increases and falls as x decreases.
To determine which graph represents the relationship y = 3x, we can utilize the concept of slope. The equation y = 3x is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope of the equation y = 3x is 3. This means that for every increase of 1 in the value of x, the value of y will increase by 3. Similarly, for every decrease of 1 in the value of x, the value of y will decrease by 3.
Now, let's look at the possible graph options:
1. A horizontal line: If the graph is a horizontal line, it means that the value of y remains the same regardless of the value of x. However, y = 3x indicates that there is a change in y for different values of x, so this option can be ruled out.
2. A vertical line: If the graph is a vertical line, it means that the value of x remains the same regardless of the value of y. Again, this does not match the relationship y = 3x, so we can eliminate this option as well.
3. A straight line with a positive slope: This is the correct option. Since the slope for y = 3x is 3, a straight line with a positive slope will represent the increasing relationship between y and x. The line will pass through the origin (0, 0), which is the y-intercept.
Therefore, the graph representing the relationship y = 3x is a straight line with a positive slope passing through the origin.