Question

Write an equation in slope-intercept form of the line with the given parametric equations. x=-3t+5 y=8t+9

Answer 1

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Answer 2

The required equation is:

$8x + 3y = 67$

Step-by-step explanation:

We are given the following in the question:

$x=-3t+5\\y=8t+9$

We have to find the equation in slope-intercept form.

$y = mx + x$

where m is the slope and c is the y intercept.

Slope, m:

$\dfrac{dy}{dt} = 8\\\\\dfrac{dx}{dt} = -3\\\\m = \dfrac{dy}{dx} = -\dfrac{8}{3}$

y-intercept, c:

When x = 0

$0=-3t+5\\\\t = \dfrac{5}{3}\\\\y = 8(\frac{5}{3})+9\\\\y = \dfrac{40}{3} + 9 = \dfrac{67}{3}$

Thus, the slope intercept form is

$y = -\dfrac{8}{3}x + \dfrac{67}{3}\\\\3y = -8x + 67\\8x + 3y = 67$

is the required equation.

#LearnMore

A line has slope 2 and y–intercept 5.  What is the equation of the line in slope intercept form?

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