What is the slope of a line that passes through the points (5, 3) and open parentheses (7, -4)?

slope is -7/2

Step-by-step explanation:

y=-4 ,y0=3, x=7, x0=5

Slope=(y-y0) ➗ (x-x0)

Slope=(-4-3) ➗ (7-5)

Slope=-7/2

this question relies purely on our observation of the graph and a knowledge of the behaviour of a graph of a hyperbola.

now, what we should realise is that there are two asymptotes - one at x = 0 and one at y = 0. what this means is that the graph will gradually approach, but never touch, these two lines. so, as x becomes more positive (ie. 'a very large positive number'), it will get closer to the line y = 0 (ie. the x-axis) - which means that the value of f(x) will gradually become smaller and closer to 0 - but will never reach it.

we can also observe this from the right half of the graph, where the graph gradually lowers closer and closer to the x-axis as x increases. what is important to note however is that it will never actually touch the x-axis (ie. f(x) will not equal 0) since there is an asymptote there. given this, we can see that option d, f(x) is a very small positive number, would be correct.

it could be a ..idk tho