Answer :
The answer for this question is A:
A = x = –t + 1 and y = 0.5t + 4 when –2 ≤ t ≤ 6
The parametric equations of the curve are:
x = –t + 1 and y = 0.5t + 4 when –5 ≤ t ≤ 3
Parametric equation of the line:
The parametric equation of the line is, [tex]x=x_0+at,y=y_0+bt[/tex] where [tex](x_0,y_0)[/tex] is the point on the line and [tex]\frac{b}{a}[/tex] is the slope of the line with a, b are real numbers.
Slope of the line:
If (a, b) and (c, d) are any two points on the line then, slope of the line is:
m = (d - b)/(c - a)
For given situation,
a line goes from (-5, 7) to (3, 3).
Using the formula of slope, the value of m i.e., slope of the line would be,
⇒ m = (7 - 3)/(-5 - 3)
⇒ m = 4/(-8)
⇒ m = 1/(-2)
⇒ m= 0.5/(-1)
Comparing with m = b/a,
b = 0.5 and a = -1.
From the graph of the line given below,
A point (1, 4) is also on the line.
Let [tex]\bold{(x_0,y_0)=(1,4)}[/tex]
Using the parametric equation of the line,
[tex]x=x_0+at[/tex]
⇒ x = 1 + (-1)t
⇒ x = -t + 1
and [tex]y = y_0+bt[/tex]
⇒ y = 4 + (0.5)t
⇒ y = 0.5t + 4
Therefore, the parametric equations of the curve are:
x = –t + 1 and y = 0.5t + 4 when –5 ≤ t ≤ 3
Learn more about the parametric equations here:
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