Question

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

Answer 1

The equation in slope-intercept from is y = $\frac{9}{8}x - \frac{3}{8}$.

Step-by-step 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 = $\frac{x-3}{8}$

Similarly,

y = 9t + 3

y - 3 = 9t

t = $\frac{y-3}{9}$

Now, comparing both equations

$\frac{x-3}{8}$ =  $\frac{y-3}{9}$

9x -27 = 8y -24

9x - 3 = 8y

or

y = $\frac{9}{8}x - \frac{3}{8}$

Hence, the equation in slope-intercept from is y = $\frac{9}{8}x - \frac{3}{8}$.