2. Write an equation in slope-intercept form of a line with the given parametric equations.
x = 9t + 2
y = 2t – 2
answer choices:
a)y=(2/9)x - (22/9)
b)y=(22/9)x + (2/9)
c) y=(9/2)x - (9/22)
d) y=(2/5)x + (2/3)
If you could show some work, because I'm pretty confused. Thank you :)
solve each for t
x = 9t+2
9t = x-2
t = (x-2)/9
y = 2t-2
2t = y+2
t = (y+2)/2
so (x-2)/9 = (y+2/2
cross-multiply
2x - 4 = 9y + 18
2x - 9y = 22--> I would have like that from
-9y = -2x + 22
y = (2/9)x - 22/9 -- looks like the a)'s have it.
Wow, Thank you so much Reiny!!
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and y-intercept (b).
Given the parametric equations:
x = 9t + 2
y = 2t - 2
1. Let's solve the first equation (x = 9t + 2) for t:
x - 2 = 9t
t = (x - 2) / 9
2. Substitute the value of t in the second equation (y = 2t - 2):
y = 2 * [(x - 2) / 9] - 2
= (2/9)(x - 2) - 2
= (2/9)x - (4/9) - (18/9)
= (2/9)x - (22/9)
So, the equation of the line in slope-intercept form is y = (2/9)x - (22/9).
Therefore, the correct answer choice is (a) y = (2/9)x - (22/9).
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the values of slope (m) and y-intercept (b).
Given the parametric equations:
x = 9t + 2
y = 2t – 2
To find the slope (m), we can compare the coefficients of t in front of x and y. The coefficient of t in front of x is 9, and the coefficient of t in front of y is 2.
So, the slope (m) of the line is given by m = 2/9.
Now, let's find the y-intercept (b). To do this, we need to find the value of y when x is equal to 0.
From the equation x = 9t + 2, we set x = 0 and solve for t:
0 = 9t + 2
9t = -2
t = -2/9
Now, substitute this value of t into the equation for y to find the corresponding y-coordinate:
y = 2t – 2
y = 2*(-2/9) – 2
y = -4/9 - 18/9
y = -22/9
So, the y-intercept (b) of the line is -22/9.
Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line using slope-intercept form:
y = (2/9)x - 22/9
Comparing this equation with the answer choices, we see that the correct answer is option (a):
y = (2/9)x - (22/9)
So, the answer is a).