91Ó°ÊÓ

For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line. $$ x=4-3 t, \quad y=-2+6 t $$

For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line. $$ x=-5 t+7, \quad y=3 t-1 $$

For the following exercises, determine the slope of the tangent line, then find the equation of the tangent line at the given value of the parameter. \(\quad x=3 \sin t, \quad y=3 \cos t, \quad t=\frac{\pi}{4}\)

For the following exercises, determine the slope of the tangent line, then find the equation of the tangent line at the given value of the parameter. \(\quad x=\cos t, \quad y=8 \sin t, t=\frac{\pi}{2}\)

For the following exercises, determine the slope of the tangent line, then find the equation of the tangent line at the given value of the parameter. \(x=2 t, \quad y=t^{3}, \quad t=-1\)

For the following exercises, determine the slope of the tangent line, then find the equation of the tangent line at the given value of the parameter. \(x=t+\frac{1}{t}, \quad y=t-\frac{1}{t}, \quad t=1\)

For the following exercises, determine the slope of the tangent line, then find the equation of the tangent line at the given value of the parameter. \(\quad x=\sqrt{t}, \quad y=2 t, \quad t=4\)

For the following exercises, find all points on the curve that have the given slope. \(\quad x=4 \cos t, \quad y=4 \sin t,\) slope \(=0.5\)

For the following exercises, find all points on the curve that have the given slope. \(\quad x=2 \cos t, \quad y=8 \sin t,\) slope \(=-1\)

For the following exercises, find all points on the curve that have the given slope. \(x=t+\frac{1}{t}, \quad y=t-\frac{1}{t},\) slope \(=1\)