Write an equation in slope-intercept form of the line with the given parametric equations?

Question

These are the two parametric equations needed for slope intercept

x=-3t+5

y=8t+9

Answer 1

Sure thing.

So we have x = -3t+5 and y = 8t+9. How can we relate these equations?

A slope-intercept equation takes the form y = mx+b, so we need to replace the "8t" in the second equation with some sort of x. We can do this by solving for t in terms of x.

With equation #1:

x-5 = -3t

-(x-5/3) = t

Now we can substitute this into the second equation.

y = 8(-(x-5)/3)+9

y = (-8x+40/3)+9

After solving, we get

y = -8x/3 + 67/3

Answer 2

Solve the first equation for t

t=(x-5)/-3

Substitute this into the second equation

y=8(x-5)/-3+9 Distribute

y=-8/3x+40/3+9 Combine like terms

y=-8/3x+67/3