The answer I got is x= -2. Am i right?

## The equation of the horizontal line that passes through the point (-2, -1).

# 3 Answers

**NO!**** The answer is y = -1. T****o understabd why, please read the following**** ****STEP BY STEP SOLUTION**

1. **Read**,
**understand**
the situation within, **identify** and pull out**
important information**.

• There are infinite lines passing through the point (-2,-1).

• There is * only one horizontal line parallel to y-axis* passing through the point (-2,-1). This line is

*, and*

**vertical to x-axis***the*

**crossing***in the*

**x-axis***.*

**x-intercept point**• There is

*passing through the point (-2,-1). This line is*

**only one horizontal line parallel to x-axis***, and*

**vertical to y-axis***the*

**crossing***in the*

**y-axis***. This is our requested parallel line passing through the point (-2,-1).*

**y-intercept point**• A line is a set of infinite points! Every point of a line is identified by its coordinates (x,y). All points of this horizontal line passing through (-2,-1)

*.*

**have the same “y”- coordinate**2. **Translate** each of the
**keywords** in the problem to their
**mathematical symbols**.

“Horizontal line” through (-2,-1): * all points have same y = -1*.

3. **Set up** and
**solve** the equation:

**y = -1** It's the equation of the horizontal line passing through (-2,-1). This equation is true only when the value of the
*coordinate y * is “-1”, for any value of "x".

4. **Verify**
your answer.

• The slope (m) of an horizontal line is 0!

**m = RISE /RUN**; m = 0 / RUN = 0

**RUN = Any**

**RISE = 0**; as you move to the right along the line, it does not rise or fall at all. In fact, when going from point P1 (-2,-1) to another point P2 (x2, y2) of the given horizontal line:

**RISE** = y2 – y1

**RISE** = (-1) - (-1) =

**RISE** = -1 + 1

**RISE = 0**.

Therefore, m = 0 / RUN

**m = 0**

• The equation of an horizontal line is a * special case of slope-intercept form* having

*, and the*

**m = 0**

**y-intercept = b****y = mx + b**;

y = 0x + (-1);

**y = -1 **(No matter what the x-value is, the y-value is always a constant value “-1”;
* “y” does not change*).

• In the** point-intercept form y - y1 = m (x - x1)** we get the same result:

y - (-1) = 0 (x - (- 2));

y + 1 = 0 ;

**y = -1**

5. **Curiosities**:

• * Standard form equation* Ax + By = C, for the horizontal line through (-2,-1):

**0x + 1y = -1**. Where A=0, B=1, C=-1 (in our case).

• The * y-intercept point* of our horizontal line is

*.*

**(0,-1)**• * Graphing* our horizontal line

**y = -1**: Plot the given point

**(-2,-1)**and the y-intercept point

**(0,-1)**. Draw a line through the points (-2,-1) and (0,-1).

• In 2-dimension geometry, * horizontal lines have not x-intercept* in the conventional sense of the words (

*) .*

**Euclidean plane**• * Mathematically*, the

*is*

**only horizontal line having infinite x-intercept points****y = 0**, because its points coincide with the points of x-axis. So the graph of the line is the x-axis, and every real number for x could be considered as an x-intercept.

• According to the * Euclid’s parallel postulate*,

*, in a*

**two parallel lines do not intersect!**However**mathematically***,*

**non-Euclidean space***So, find the x-intercept point for our given horizontal line. Think for a while (?)*

**parallel lines intersect only at the infinity!**

A horizontal line runs left to right or vice versa like so

<--------------------------->

which means that the line will cross on the y axis and the point -1 lies on the y axis. This line will never touch the x axis. It will run straight 1 unit below the x axis forever and crossing only y.

No, and this is why.

If you were to plot that point, you would start at the origin and go left two, down one.

Looking at the Cartesian Plane, a horizontal line going through that point would occur at y = -1