Find a set of parametric equations for y= 3x + 7, given the parameter t= 5 – 5x
from
t= 5 – 5x
5x = 5 - t
x = (5-t)/5
so in y = 3x+7
y = 3(5-t)/5 + 7
5y = 15 - 3t + 35
y = - 3t/5 + 10
x = (5-t)/5
y = - 3t/5 + 10
Well, let's see if I can put a funny spin on this. How about this:
I present to you the clownish parametric equations for y = 3x + 7:
x = t/5
y = 3(t/5) + 7
Remember, laughter is the best mathematical medicine!
To find a set of parametric equations for y = 3x + 7, given the parameter t = 5 - 5x, we can equate t to 5 - 5x and solve for x. Once we find the value of x, we can substitute it back into the equation y = 3x + 7 to find the corresponding value of y. Thus, the set of parametric equations can be written as:
x = (5 - t) / 5
y = 3x + 7
Let's break it down step-by-step:
Step 1: Equate t to 5 - 5x and solve for x:
t = 5 - 5x
5x = 5 - t
x = (5 - t) / 5
Step 2: Substitute the value of x into the equation y = 3x + 7:
y = 3((5 - t) / 5) + 7
Step 3: Simplify the equation:
y = (15 - 3t) / 5 + 7
y = (15 - 3t + 35) / 5
y = (50 - 3t) / 5
Therefore, the set of parametric equations for y = 3x + 7, given the parameter t = 5 - 5x, is:
x = (5 - t) / 5
y = (50 - 3t) / 5
To find a set of parametric equations for the given equation y = 3x + 7, we need to express both x and y in terms of a common parameter, which is t in this case.
Given that t = 5 - 5x, we can solve for x in terms of t:
t = 5 - 5x
5x = 5 - t
x = (5 - t) / 5
Now, we substitute this value of x back into the equation y = 3x + 7 to express y in terms of t:
y = 3x + 7
y = 3((5 - t) / 5) + 7
y = (15 - 3t) / 5 + 7
y = (15 - 3t + 35) / 5
y = (50 - 3t) / 5
Therefore, the set of parametric equations for y = 3x + 7, given the parameter t = 5 - 5x, is:
x = (5 - t) / 5
y = (50 - 3t) / 5