Answer:
Slope intercept form: The straight line equation is given by:
[tex]y-y_1=m(x-x_1)[/tex], .....[1] where m is the slope of the line.
(A)
Let x represents the number of hours and y represents the velocity of the runner.
As per the statement: After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.
we have two points as (1, 5) and (3, 3)
Calculate first slope.
Formula for slope(m) is given by;
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Then substitute the given values we get;
[tex]m = \frac{3-5}{3-1} = \frac{-2}{2} =-1[/tex]
Now, substitute the value of m = -1 and (1, 5) in equation [1] we have;
[tex]y-5=-1(x-1)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
[tex]y-5 = -x + 1[/tex]
Add both sides by 5 we get;
[tex]y = -x + 6[/tex]
or
[tex]x+ y = 6[/tex]
Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times is, [tex]x+ y = 6[/tex]
(B)
x y = 6 -x
1 5
2 4
3 3
4 2
5 1
Now, plot these points on the graph for the first 5 hours as shown below in the attachment.
