Consider the line defined by the parametric equations x=3d-10, y=2d+1.
The y-intercept of this line can be expressed as a/b. Find a and b.
from x = 3d-10 ---> d = (x+10)/3
from y = 2d+1 ---> d = (y-1)/2
then (x+10)/3 = (y-1)/2
2x + 20 = 3y - 3
2x - 3y = -23
for y-intercept, x = 0
-3y = -23
y = 23/3 = a/b
or
in x=3d-10 , let x = 0
3d = 10
d = 10/3
sub into y = 2d+1
= 2(10/3)+1 = 23/3 = a/b
To find the y-intercept of the line defined by the given parametric equations, we need to find the value of y when x is equal to 0.
First, let's set x=0 in the equation x=3d-10:
0 = 3d - 10
Now, solve for d:
3d = 10
d = 10/3
Next, substitute d = 10/3 into the equation for y:
y = 2(10/3) + 1
y = 20/3 + 1
y = 20/3 + 3/3
y = 23/3
Therefore, the y-intercept of the line can be expressed as a fraction a/b, where a = 23 and b = 3.