Question

Given the function f(x) = 6x + 1 and the linear function g(x), which function has a greater slope?

Image is an positive linear function increasing through 2 comma 3 and 3 comma 7

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

Answer 1

The function f(x) = 6x + 1 has a greater slope than the linear function g(x) represented in the image. After calculating, we find that f(x) has a slope of 6, while g(x) has a slope of 4, confirming that f(x) has the steeper ascent.

Step-by-step explanation:

To determine which function has a greater slope, we compare the slope of the given function f(x) = 6x + 1 with the slope of the linear function g(x) represented in the image. The slope of f(x) is the coefficient of x, which is 6. To find the slope of the linear function g(x), we can use two given points from the image: (2, 3) and (3, 7).

To calculate the slope (m) of g(x), we use the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (7 - 3) / (3 - 2) = 4 / 1 = 4. Since f(x) has a slope of 6 and g(x) has a slope of 4, it is clear that f(x) has a greater slope than g(x).