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,

x = 8t+3

y= 9t+3

First, convert both the equations in terms of t for comparison.

x = 8t + 3

x - 3 = 8t

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

Similarly,

y = 9t + 3

y - 3 = 9t

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

Now, comparing both equations

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

9x -27 = 8y -24

9x - 3 = 8y

or

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

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