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

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

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

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James Z. | Chemistry/Math/Biology TutorChemistry/Math/Biology Tutor

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

**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

• There is

• 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)

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

**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

• * Graphing* our horizontal line

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

• * Mathematically*, the

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

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.

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