Answer:
here we have:
x = 5*t + 3
y = 2*t - 6
both for -2 ≤ t ≤ 3
First, we can rewrite:
x = a*y + b
let's try to find the values of a and b.
5*t + 3 = a*(2*t - 6) + b
5*t + 3 = a*2*t + (b - 6*a)
Here we have two equations:
5 = a*2
3 = (b - 6*a)
from the first one, we can solve:
5/2 = a
replacing this into the second, we et:
3 = b - 6*(5/2)
3 = b - 15
3 + 15 = b = 18
Then:
x = (5/2)*y + 18
y = 2*t - 6
So, y is a linear equation that depends on the variable t
x is a linear equation that only depends on x (from this we already know that the graph will be a line)
and we know that −2 ≤ t ≤ 3
Then the minimum value of y is:
y = 2*(-2) - 6 = -10
and the largest value of y is:
y = 2*3 - 6 = 0
So y-varies in the range between -10 and 0
And because x = (5/2)*y + 18
The minimum value of x is:
x = (5/2)*-10 + 18 = -25 + 18 = -7
and the maximum value of x is:
x = (5/2)*0 + 18 = 18
Then we know that this line starts in the point (-10, -7) and ends in the point (0, 18)
