Which rule matches the function shown in the graph
Y=3x
Y=x+2
Y=x-2
Y=x/3
The rule that matches the function shown in the graph is Y=3x.
To determine which rule matches the function shown in the graph, we need to analyze the slope and y-intercept of the line on the graph.
In the graph, the line passes through the origin (0,0) and has a positive slope. This means the line rises as x increases.
Let's evaluate each rule to see which one matches the given graph:
1. Y = 3x:
- This rule represents a line with a slope of 3 and a y-intercept of 0. This matches the graph, as it has a positive slope and goes through the origin.
2. Y = x + 2:
- This rule represents a line with a slope of 1 and a y-intercept of 2. Since the graph does not intersect the y-axis at (0,2), this rule does not match the graph.
3. Y = x - 2:
- This rule represents a line with a slope of 1 and a y-intercept of -2. Again, since the graph does not intersect the y-axis at (0,-2), this rule does not match the graph.
4. Y = x/3:
- This rule represents a line with a slope of 1/3 and a y-intercept of 0. Since the slope of the graph is not 1/3, this rule does not match the graph.
Therefore, the rule that matches the function shown in the graph is Y = 3x.