1. What is an equation for the line with slope \(\frac{2}{3}\) that passes through \((6,8)?\) Write it in both forms \(y = mx+b\) and \(Ax + By = C.\)
2. What is an equation for the line that passes through the points \((-3,2)\) and \((3,6)?\)
3. What is an equation for the line that’s parallel to \(y = \frac{2}{3}x+4\) that passes through the point \((3,-5)?\)
4. What is an equation for the line that’s perpendicular to \(y = \frac{2}{3}x+4\) that passes through the point \((3,-5)?\)
5. The unit circle is the circle of radius 1 centered at the origin. Its equation is \(x^2+y^2 = 1.\)
   1. What are the coordinates of the point where does the line \(y=x\) intersect the top half of the unit circle?
   2. What are the coordinates of the point where does the line \(y=2x\) intersect the top half of the unit circle?
   3. What are the coordinates of the point where does the line \(y=\frac{1}{2}x\) intersect the top half of the unit circle?
6. A line is tangent to a circle at a point if it “touches” the circle at only that one point, not crossing into the interior of the circle. First confirm that the point \((8,15)\) lies on the circle with equation \(x^2+y^2 = 289.\) Then find an equation for the line tangent to the circle at this point. Hint: Sketch a picture of circle and line in question, and add the line segment connecting the origin to the point \((8,15)\) to your sketch. What’s the slope of this segment? What’s must the slope of the line be? .