Find the parametric equations of a line that passed through point (2,-9) and has slope -3/4. Assume t = 0 corresponds to the given point, t increases as x increases, and that the speed is sqrt(25).
x(t) =
y(t) =
+130516 Since the starting point is (-2, 9), the slope is -3/4, and t increases as x increases, we have....
x(t) = -2 + 3t
y(t) = 9 - 4t
Notice that when t = 1, x = 1 and y = 5
And the distance between the ponts is √[(-2 -1)^2 + (9 - 5)^2] = √[3^2 + 4^2] = √25......which means that some object traveling on this line starting at (-2,9) and moving at this speed (per some time unit) will reach (1, 5) after one of these time units.....just what we want....!!!
+130516 Since the starting point is (-2, 9), the slope is -3/4, and t increases as x increases, we have....
x(t) = -2 + 3t
y(t) = 9 - 4t
Notice that when t = 1, x = 1 and y = 5
And the distance between the ponts is √[(-2 -1)^2 + (9 - 5)^2] = √[3^2 + 4^2] = √25......which means that some object traveling on this line starting at (-2,9) and moving at this speed (per some time unit) will reach (1, 5) after one of these time units.....just what we want....!!!
