Lesson 9

\(3x-2y=6\)

\(y=\frac{3}{2}x+3\)

\(y=\frac{3}{2}x-3\)

\(y-3=\frac{3}{2}(x-4)\)

\(y-6=\frac{3}{2}(x-2)\)

A line with slope \(\frac32\) passes through the point \((1,3)\).

1. Explain why \((3,6)\) is on this line.
2. Explain why \((0,0)\) is not on this line. 
3. Is the point \((13,22)\) on this line? Explain why or why not.

Write an equation of the line that passes through \((1,3)\) and has a slope of \(\frac{5}{4}\).

A parabola has focus \((3,\text{-}2)\) and directrix \(y=2\). The point \((a,\text{-}8)\) is on the parabola. How far is this point from the focus?

6 units

8 units

10 units

cannot be determined

Write an equation for a parabola with each given focus and directrix.

1. focus: \((5, 2)\); directrix: \(x\)-axis
2. focus: \((\text{-}2, 3)\); directrix: the line \(y=7\)
3. focus: \((0,7)\); directrix: \(x\)-axis
4. focus: \((\text{-}3, \text- 4)\); directrix: the line \(y=\text-1\)

A parabola has focus \((\text{-}1,6)\) and directrix \(y=4\). Determine whether each point on the list is on this parabola. Explain your reasoning.

1. \((\text{-}1,5)\)
2. \((1 ,7)\)
3. \((3, 9)\)

Select the center of the circle represented by the equation \(x^2 + y^2 - 8x + 11y - 2 = 0\).

\((8, 11)\)

\((4, 5.5)\)

\((\text-4, \text-5.5)\)

\((4, \text-5.5)\)