A 2-dimensional graph of a straight line having points labeled A, B,C, intersecting the vertical axis at point B and the horizontal axis at point A. Point A is at left-parenthesis negative 1 comma 0 right-parenthesis, point B is at left-parenthesis 0 comma 2 right-parenthesis, and point C is at left-parenthesis 1 comma 4 right-parenthesis.
As x increases by 1, y increases by 3.
A. The slopes are equal.
B. The graph has a greater slope.
C. The function rule has a greater slope.
D. none of the above
The slope of a line is defined as the change in y divided by the change in x (rise over run). Using points A and B, the slope of the line can be calculated as (2-0)/(0-(-1)) = 2/1 = 2.
Using points B and C, we can calculate the slope of the line as (4-2)/(1-0) = 2/1 = 2.
Since the slopes are equal, the correct answer is A. The slope of the line and the slope of the function rule are also equal, as they describe the same line.
The statement "As x increases by 1, y increases by 3" indicates that the slope of the line is equal to 3.
To find the slope of a line, we can use the formula:
slope = (change in y) / (change in x)
In this case, the change in y is 2 - 0 = 2, and the change in x is 0 - (-1) = 1.
slope = 2 / 1 = 2
Since the slope of the line is equal to 3, and the slope of the function rule is 2, the correct answer is:
D. none of the above