Question

Part A: The graph of which equation below is a horizontal line?

1) x + y = 3
2) y = 3
3) x = 3
4)x/y = 3
Part B: Explain in 3-4 sentences why your equation in Part A is horizontal line. Your answer should include at least 4 of the following words:
x-coordinate
y-coordinate
ordered pair slope y-intercept
slope-intercept form

Answer 1

For 2)
`y = 3`

is a Horizontal Line withe Explanation as below.

Explanation:

Given:

1) x + y = 3

2) y = 3

3) x = 3

4)x/y = 3

Solution:

Part A:

Slope of horizontal line is 0. So, equation of line is of the form y = b

Now, from all the options available, option 2 matches the definition.

Part B: Following are the properties of a horizontal line.

1. Parallel to x axis.

2. The y-coordinate is always the same .

3. The x-coordinate only changes.

4. The slope is zero .

So, the equation is of the form y = b

Where 'b' is the value of the y coordinate.

5. The ordered pair is (x,b)

6. Slope-intercept form is given as

`y=mx+c`

where m = slope

c = y - intercept

So for horizontal line slope is zero

∴ y = 0 × x +c = c

∴ y = c

∴ y = 3 is a Horizontal line