Answer:
Part 1) the linear equation is [tex]y=1.75x+16[/tex]
Part 2) The graph in the attached figure
Step-by-step explanation:
Part 1) Write an equation
Let
x ----> the time in seconds
y ----> the distance in feet that the kite is from the end of your hands
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value
In this problem
we have
[tex]m=1.75\ \frac{ft}{sec}[/tex]
[tex]point\ (8,30)[/tex]
substitute
[tex]30=1.75(8)+b[/tex]
solve for b
[tex]30=14+b[/tex]
[tex]b=30-14[/tex]
[tex]b=16\ ft[/tex] ----> the initial distance
therefore
The linear equation is equal to
[tex]y=1.75x+16[/tex]
Part 2) Graph the equation
we have
[tex]y=1.75x+16[/tex]
To graph the line we need two points
we have
(0,16) and (8,30)
Plot the points and connect them to graph the line
Remember that the values of x and y cannot be a negative number
The graph in the attached figure
