Write an equation in slope–intercept form of the line with the given parametric equations.
x = 9t + 2
y = –6t + 9
Answer Choices
(A) y=-2/3x-3/7 (B) y=-3/2x+3/31
(C) y=31/3x-2/3 (D) y=-2/3x+31/3
y = - ( 2 / 3 ) ( x - 2 ) + 9
y = - ( 2 / 3 ) x - ( 2 / 3 ) * ( - 2 ) + 9
y = - ( 2 / 3 ) x + 4 / 3 + 9
y = - ( 2 / 3 ) x + 4 / 3 + 27 / 3
y = - ( 2 / 3 ) x + 31 / 3
Answer D
x = 9t+2 --> t = (x-2)/9
y = -6t+9 --> t = (9-y)/6
then : (x-2)/9 = (9-y)/6
6x-12 = 81-9y
9y = -6x + 93
y = (-2/3)x + 31/3
looks like B)
You are right Bosnian, it is D
Time to clean my glasses, lol
wait nvm it's D, I'd delete my previous post but dont know how
To convert the given parametric equations into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, follow these steps:
1. Start with the given parametric equations:
x = 9t + 2
y = -6t + 9
2. Solve the first equation for t:
x = 9t + 2
Subtract 2 from both sides:
x - 2 = 9t
Divide both sides by 9:
(x - 2)/9 = t
3. Substitute the value of t in the second equation:
y = -6t + 9
Replace t with (x - 2)/9:
y = -6((x - 2)/9) + 9
Simplify:
y = (-6x + 12)/9 + 9
y = (-6x + 12)/9 + 81/9
y = (-6x + 12 + 81)/9
y = (-6x + 93)/9
4. Simplify the equation:
y = (-6x + 93)/9
Divide both the numerator and denominator by 3:
y = (-2x + 31)/3
Therefore, the equation in slope-intercept form is y = (-2/3)x + 31/3.
x = 9 t + 2
x - 2 = 9 t
( x - 2 ) / 9 = t
t = ( x - 2 ) / 9
y = – 6 t + 9
y = - 6 * ( x - 2 ) / 9 + 9
y = - 3 * 2 * ( x - 2 ) / ( 3 * 3 ) + 9
y = - ( 2 / 3 ) ( x - 2 ) + 9