Question

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Given the function f(x) = 3x + 1 and the linear function g(x), which function has a greater slope?

positive linear function increasing through 2 comma 3 and 3 comma 7

A. f(x) has a greater slope.
B. g(x) has a greater slope.
C. The slopes of f(x) and g(x) are the same.
D. The slope of g(x) is undefined.

Answer 1

B. Is the correct option

Answer 2

To find the slope of a linear function, we can use the formula:

Slope=Change in xChange in y​=x2​−x1​y2​−y1​​

where (x1​,y1​) and (x2​,y2​) are any two points on the line



In this question, we are given the function f(x)=3x+1 and the graph of another linear function g(x).

To find the slope of f(x), we can use any two points on its graph. For example, we can use (0,1) and (1,4), which are obtained by plugging in x=0 and x=1 into f(x). Then we apply the slope formula:

Slope of f(x)=1−04−1​=13​=3

To find the slope of g(x), we can use the two points given in the image: (2,3) and (3,7). Then we apply the slope formula:

Slope of g(x)=3−27−3​=14​=4

Now we can compare the slopes of f(x) and g(x). We see that 4>3, so g(x) has a greater slope than f(x). Therefore, the correct answer is B. g(x) has a greater slope