98 points and brainliest for best marion is observing the velocity of a cyclist at different times. after two hours, the velocity of the cyclist is 18 km/h. after four hours, the velocity of the cyclist is 4 km/h. part a: write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. show your work and define the variables used. (5 points) part b: how can you graph the equations obtained in part a for the first 8 hours? (5 points)

A) We are told that at 2 hours, the velocity is 18 km/h and at 4 hours, the velocity is 4 km/h. Since we are relating two variables - let's give them names.

Let x = time and y = velocity. Since the velocity depends on the time (that is, the time influences velocity), this is a linear function. Any linear function can be written in slope intercept form as y = mx + b. The problem wants the situation in standard from of Ax + By = C, which can be found from slope intercept form.

So now we can make our line. Consider the ordered pairs of (2,18) and (4, 4) with them in (x, y) form. Finding the slope, m, between these points is as such:

m = y₂-y₁ / x₂-x₁

m = 4 - 18 / 4 - 2

m = -14 / 2 = -7.

Our slope is -7.

We take m = -7, x = 4, and y = 4 (it goes 4 km/h in 4 hrs) and use those three things to find the y-intercept.

y = mx + b

4 = -7 * 4 + b

4 = -28 + b

32 = b

So our equation of the line is y = -7x + 32. To put the equation into standard form, we need to place all the variables on one side of the equals sign, all the numbers on the other.

y = -7x + 32

7x + y = 32

In standard form, the equation for this situation is 7x + y = 32

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To find out the velocity at 8 hours, we evaluate our function at x = 8. Either equation (standard form or slope intercept) works; we use standard form.

7x + y = 32

7*8 + y = 32

56 + y = 32

y = -24

At a time of eight hours, the bicycle is moving at -24 km/h.