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?
