Question

Write an equation in slope-intercept form of the line with the parametric equations x=9t and y=4t+2 .

Answer 1

$9t=x\qquad\text{divide both sides by 9}\\\\t=\dfrac{x}{9}\to t=\dfrac{1}{9}x\\\\\text{substitute to}\ y=4t+2\\\\y=4\left(\dfrac{1}{9}x\right)+2\\\\\boxed{y=\dfrac{4}{9}x+2}$

Answer 2

Answer:

The required equation in slope-intercept form is $y=\frac{4}{9}x+2$

Step-by-step explanation:

Given : The parametric equations $x=9t$ and $y=4t+2$

To find : Write an equation in slope-intercept form of the line?

Solution :

The parametric equations were re-written in terms of t is

$t=\frac{x}{9}$

and $t=\frac{y-2}{4}$

Now, equating both t we get,

$\frac{x}{9}=\frac{y-2}{4}$

$4x=9(y-2)$

$4x=9y-18$

Separate y from the equation to form slope-intercept form

$4x+18=9y$

$y=\frac{4x+18}{9}$

$y=\frac{4x}{9}+2$

The slope intercept form is $y=mx+b$

where, m is the slope of line and b is the y-intercept.

So, The required equation in slope-intercept form is $y=\frac{4}{9}x+2$