Asap, will mark (only comment if you know how to solve ) sam is observing the velocity of a car at different times. after three hours, the velocity of the car is 53 km/h. after six hours, the velocity of the car is 62 km/h. part a: write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. show your work and define the variables used. part b: how can you graph the equation obtained in part a for the first seven hours?

1) We are told that at 3 hours, the velocity is 53 km/h and at 6 hours, the velocity is 62 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 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 (3, 53) and (6, 62) with them in (x, y) form. Finding the slope, m, between these points is as such:

m = y₂-y₁ / x₂-x₁

m = 62-53 / 6-3

m = 9/3 = 3.

Our slope is 3.

We take m = 3, x = 3, and y = 52 (the goes 52 km/h in 3 hrs) and use those three things to find the y-intercept.

y = mx + b

53 = 3 * 3 + b

53 = 9 + b

44 = b

So our equation of the line is y = 3x + 44. 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 = 3x + 44

-3x + y = 44

3x - y = -44 (multiply through by -1)

So with x = time, y = velocity we have 3x - y = -44 as the standard form to represent this scenario.

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To find out the velocity at 7 hours, we evaluate our function at x = 7. Either equation (standard form or slope intercept) works; we use standard form.

3x - y = -44

3(7) - y = -44

21 - y = -44

-y = -65

y = 65

At a time of seven hours, the velocity is 65 km/h.

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