Question

Write an equation in slope-intercept form of the line with parametric equations: x=−3t−7 and y=−2t+6

a) y=−2x+8
b) y=2x+8
c) y=−2x−8
d) y=2x−8

Answer 1

The equation in slope-intercept form of the line with parametric equations is y = -2x / 3 + 32 / 3.

Step-by-step explanation:

The given parametric equations are:

x = -3t - 7

y = -2t + 6

To write the equation in slope-intercept form, we need to solve for t in terms of x and y. We can start by isolating t in the first equation:

t = (-x - 7) / 3

Substitute this value of t into the second equation:

y = -2((-x - 7) / 3) + 6

Simplify the expression:

y = (-2x + 14) / 3 + 6

y = -2x / 3 + 14 / 3 + 6

y = -2x / 3 + 32 / 3

This is the equation in slope-intercept form, where the slope is -2/3 and the y-intercept is 32/3.