How does the graph of line f compare to the graph of the line ?
f(x) = 2/3x - 7
g(x) = 3/2x - 7
A. The two line are parallel.
B. Line g is steeper than line f,
C. The graph of f has a different y-int than the graph of f.
D. Line f is steeper than line g.
The correct answer is C. The two lines have the same slope, which is 2/3, but different y-intercepts. The y-intercept for f(x) is -7, while the y-intercept for g(x) is also -7.
To compare the graphs of the two lines, let's look at their slope and y-intercept:
The given functions are:
f(x) = (2/3)x - 7
g(x) = (3/2)x - 7
We can observe that both lines have the same y-intercept, which is -7. Therefore, option C is incorrect.
Now let's compare the slopes of the two lines:
The slope of f(x) is 2/3.
The slope of g(x) is 3/2.
Since the slope of g(x) is larger than the slope of f(x), we can deduce that g(x) is steeper than f(x). Thus, option B is correct.
Therefore, the correct answer is:
B. Line g is steeper than line f.
To compare the graphs of lines f(x) = (2/3)x - 7 and g(x) = (3/2)x - 7, we need to analyze their characteristics such as slope and y-intercept.
First, let's consider the slope of each line. The coefficient of x represents the slope of a line in the slope-intercept form (y = mx + b), where m is the slope. For line f, the slope is 2/3, and for line g, the slope is 3/2.
Option B states that "Line g is steeper than line f." However, this is not true because a larger slope means a steeper line. Comparing the slopes, we can see that 2/3 (line f) is less than 3/2 (line g). Therefore, option B is incorrect.
Next, let's determine if the two lines are parallel or not. Two lines are parallel if they have the same slope. Since the slopes of line f and line g are not equal (2/3 ≠ 3/2), we can conclude that the two lines are not parallel. Thus, option A is false.
Now, let's examine the y-intercepts of both lines. The y-intercept represents the point where the line crosses the y-axis. For line f, the y-intercept is -7, and for line g, the y-intercept is also -7. Hence, both lines have the same y-intercept, meaning option C is incorrect.
Finally, let's compare the slopes one more time. From our earlier analysis, we found that line f has a slope of 2/3, which is less than the slope of line g (3/2). As a result, we can conclude that "Line f is steeper than line g," and therefore, option D is accurate.
To summarize, the correct statement is:
D. Line f is steeper than line g.