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

**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!**