Answer:
As per the statement: Sandy is observing the velocity of a runner at different times.
Also, after one hour, the velocity of the runner is 4 km/h. and after two hours, the velocity of the runner is 2 km/h..
(A)
Let x represents the time in hours and y represents the velocity of the runner(in km/hr)
Then, we have two points from the given statement:
(1, 4) and (2, 2)
An equation of line for two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by;
[tex]y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
For the given two points (1, 4) and (2, 2) we have an equation:
[tex]y-4 = \frac{2-4}{2-1}(x-1)[/tex]
[tex]y-4 = \frac{-2}{1}(x-1)[/tex]
or
[tex]y-4 = -2(x-1)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]
[tex]y-4 = -2x + 2[/tex]
Add 4 on both sides we get;
[tex]y-4 +4= -2x + 2+4[/tex]
Simplify:
[tex]y= -2x + 6[/tex]
Add 2x on both sides we get;
[tex]y + 2x=-2x+6+ 2x[/tex]
Simplify:
[tex]y + 2x = 6[/tex]
[Since, standard form for linear equations in two variables is Ax+By=C]
Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times is:
[tex]2x+y= 6[/tex] ; where x represents the time in hours and y represents the velocity of the runner.
(B)
Equation in part A
It is given as; [tex]2x+y= 6[/tex] .....[1]
To graph this equation; for the first 4 hours.
x y = -2x+6
1 4
2 2
3 0
4 -2
Now, using these points (1, 4) , (2, 2) , (3, 0) and (4, -2) plot the graph as shown below in the attachment.
