Which rule matches the function shown in the graph
Y=3x
Y=-3x
Y=x-2
Y=x+2
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 function. Let's consider each rule one by one.
1. Y = 3x: This rule represents a linear function with a slope of 3 and a y-intercept of 0 (no constant term). To graph this function, you would plot the point (0, 0) on the y-axis as the y-intercept and then use the slope of 3 to draw a straight line passing through the origin (0, 0).
2. Y = -3x: Similar to the previous rule, this represents a linear function with a slope of -3 and a y-intercept of 0. The difference is that the slope is negative, which means the line will have a negative slope and slope downwards. The graph will also pass through the origin (0, 0).
3. Y = x - 2: This rule represents a linear function with a slope of 1 (coefficient of x) and a y-intercept of -2 (constant term). To graph this function, you would plot the point (0, -2) on the y-axis as the y-intercept and then use the slope of 1 to draw a straight line passing through this point.
4. Y = x + 2: Similar to the previous rule, this represents a linear function with a slope of 1 and a y-intercept of 2. The graph will pass through the point (0, 2), and the line will have a positive slope.
By comparing the information from the graph to the rules given, we can see that the function Y = 3x matches the graph if it represents a line with a positive slope passing through the origin.