Write an equation in slope-intercept form of the line whose parametric equations are:
x = (1/2)t +2/3 and y = t - 3/4.
a) y = 2x - 7/12
b) y = 2x + 7/12
c) y = -2x - 7/12
d) y = -2x - 25/12
I think it is D.....?
my equation is
y = 2x - 25/12
I tested it using t=0, so a point on it would be (2/3, -3/4)
none of the answers you give have that point on it, but my equation does.
check your typing.
never mind, i was right
I would proceed to eliminate t from the two equations by subtracting 2 times equation 1 from the second.
This gives me
y=2x-25/12
which does not correspond to any of the answers. So could you please check if the two equations have been entered correctly, or if the answers have been transcribed correctly.
To find the equation of a line in slope-intercept form, we need to express it as y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Given the parametric equations: x = (1/2)t +2/3 and y = t - 3/4, we can solve for t in terms of x using the equation for x.
x = (1/2)t + 2/3
Subtract 2/3 from both sides to isolate t:
x - 2/3 = (1/2)t
Multiply both sides by 2 to eliminate the fraction:
2(x - 2/3) = t
Simplify:
2x - 4/3 = t
Now that we have t expressed in terms of x, we can substitute it into the equation for y:
y = t - 3/4
Replace t with 2x - 4/3:
y = (2x - 4/3) - 3/4
Combine like terms:
y = 2x - 4/3 - 3/4
To add fractions, we need a common denominator, which is 12:
y = 2x - (16/12) - (9/12)
Combine the numerators:
y = 2x - 25/12
Comparing the equation y = 2x - 25/12 with the given options, we can see that the correct answer is:
d) y = -2x - 25/12
So, the equation in slope-intercept form of the line with the given parametric equations is y = -2x - 25/12.