Question

A the slope of f(x) is greater than the slope of g(x)

Answer 1

To find the slope of g(x), use the slope formula(m):

$m=\frac{y_2-y_1}{x_2-x_1}$        And plug in two points, I will use:

(0, 2) = (x₁, y₁)

(5, 4) = (x₂, y₂)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4-2}{5-0}$

$m=\frac{2}{5}$

You could do the same to find f(x) by finding two points and using the slope formula, or you could use this to tell visibly:

$m=\frac{rise}{run}$

Rise is the number of units you go up(+) or down(-) from each distinguished point

Run is the number of units you go to the right from each distinguished point

If you look at the graph, you can see the points (0, -1) and (3, 1). From each point, you go up 2 units and to the right 3 units (you can make sure by using another point). So the slope of f(x) is  $\frac{2}{3}$

Whichever line looks more vertical(and is positive) has the greater slope. So the slope of f(x) is greater than the slope of g(x). The answer is option A