Identify the pair of points that can represent an increasing function that has a greater rate of change than that of the function Y=8/5x+ 3/5

A general lineal equation is written as:

y = a*x +b

Where a is the slope (also called the rate of change) and b is the y-intercept-

For a line that passes through the points (x1, y1) and (x2, y2)

The slope will be:

a = (y2 - y1)/(x2 - x1)

For the line:

Y= (8/5)*x+ 3/5

The slope, or rate of change, is 8/5.

Then we want to find two points (x1, y1) and (x2, y2) such that the slope generated by them is larger to 8/5.

There are a lot of ways to finding these points, a simple way is:

We could define (x1, y1) = (0, 0)

And (x2, y2) = (5, 9)

Then the rate of change of the line that passes through these two points will be

a = (9 - 0)/(5 - 0) = 9/5

Which is larger than 8/5, as we wanted.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).