# Lesson 9

Equations of Lines

- Let’s investigate equations of lines.

### Problem 1

Select **all** the equations that represent the graph shown.

\(3x-2y=6\)

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

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

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

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

### Problem 2

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

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

### Problem 3

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

### Problem 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

### Problem 5

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

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

### Problem 6

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.

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

### Problem 7

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

\((8, 11)\)

\((4, 5.5)\)

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

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

### Problem 8

Reflect triangle \(ABC\) over the line \(x=\text-6\).

Translate the image by the directed line segment from \((0,0)\) to \((5,\text-1)\).

What are the coordinates of the vertices in the final image?