Question

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

x = 8t+3
y = 9t+ 3

Answer 1

The equation in slope-intercept from is
`y = (9)/(8)x - (3)/(8)`.

Explanation:

Given that,

x = 8t+3

y = 9t+ 3

Now, getting the value of t on both side to compare the equations.

`x = 8t+3`

`x -3 = 8t`

`t = (x-3)/(8)`

also

`y = 9t+ 3`

`t= (y-3)/(9)`

Now, by comparing the values of t, we get

`(x-3)/(8) = (y-3)/(9)`

`9x - 27 = 8y -24`

`9x - 3 = 8y`

`y = (9)/(8)x - (3)/(8)`

Hence, the equation in slope-intercept from is
`y = (9)/(8)x - (3)/(8)`.