State th coordinates of two points on the following line
x=3-8t
y=4t
For one point I got (3,0). In the back of the book it says (11, -4) for another point. How would I get that?
b) r = (4,0) + t(0, 5)
I got (4,0) for one point. In the back of the book it says (4,10) for another point. How would I get that?
To find the coordinates of the second point on the line given by the equation x = 3 - 8t and y = 4t, you need to substitute a value of t other than what you used to find the first point.
1. For the given line equation, you found the first point to be (3, 0) by setting t = 0. Now, let's substitute a different value of t, such as t = 1, into the equations and solve for x and y.
x = 3 - 8(1) = 3 - 8 = -5
y = 4(1) = 4
Therefore, when t = 1, the coordinates of the second point on the line are (-5, 4).
2. Similarly, for the line equation r = (4, 0) + t(0, 5), you found the first point to be (4, 0) by setting t = 0. Now, let's substitute a different value of t, such as t = 2, into the equation and solve for r.
r = (4, 0) + 2(0, 5) = (4, 0) + (0, 10) = (4, 0) + (0, 10) = (4, 10)
Therefore, when t = 2, the coordinates of the second point on the line are (4, 10).