# Lesson 10

Parallel Lines in the Plane

- Let’s investigate parallel lines in the coordinate plane.

### Problem 1

Select **all** equations that are parallel to the line \(2x + 5y = 8\).

\(y=\frac{2}{5}x + 4\)

\(y=\text-\frac{2}{5}x + 4\)

\(y-2=\frac{5}{2}(x+1)\)

\(y-2=\text-\frac{2}{5}(x+1)\)

\(10x+5y=40\)

### Problem 2

Prove that \(ABCD\) is not a parallelogram.

### Problem 3

Write an equation of a line that passes through \((\text-1,2)\) and is parallel to a line with \(x\)-intercept \((3,0)\) and \(y\)-intercept \((0,1)\).

### Problem 4

Write an equation of the line with slope \(\frac23\) that goes through the point \((\text-2, 5)\).

### Problem 5

Priya and Han each wrote an equation of a line with slope \(\frac13\) that passes through the point \((1,2)\). Priya’s equation is \(y-2 = \frac13 (x-1)\) and Han’s equation is \(3y - x = 5\). Do you agree with either of them? Explain or show your reasoning.

### Problem 6

Match each equation with another equation whose graph is the same parabola.

### Problem 7

A parabola is defined as the set of points the same distance from \((\text-1, 3)\) and the line \(y=5\). Select the point that is on this parabola.

\((\text-1, 3)\)

\((0, 5)\)

\((3,0)\)

\((0,0)\)

### Problem 8

Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.

- \((x,y) \rightarrow (2x,y+2)\)
- \((x,y) \rightarrow (2x,2y)\)
- \((x,y) \rightarrow (x+2,y+2)\)
- \((x,y) \rightarrow (x-2,y)\)