# Lesson: Writing Equations

## Comment on Writing Equations

### For the practice question

For the practice question with the coordinates (1,-2) (4,7). How did you get B = -5? I got Y=3X+B and when I plugged in the first coordinates, I got Y=3(1)+-2 = 1. And for the second coordinates I got Y=3(4)+7 = 17. Or did I miss a step? Thanks!
-Yvonne

### You're referring to the

You're referring to the additional practice questions that start at 3:10 in the video.

It looks like you correctly determined that the slope = 3, which means the equation (so far) is y = 3x +b

To find the value of b (the y-intercept), we plug in one set of coordinates.

IMPORTANT: the coordinates of the point (1, -2) represent x = 1 and y = -2. More importantly, since that point is on the line, those values (when plugged into the equation) must satisfy the equation.

So, take your preliminary equation, y = 3x +b, and replace x with 1 and y with -2 to get: -2 = 3(1) + b

Evaluate to get: -2 = 3 + b, which means b = -5

So, the equation of the line is y = 3x - 5

You were replacing x with 1, and (incorrectly) replacing B with -2. You should have been replacing y with -2.

### I am not able to visualise

I am not able to visualise why coordinates will satisfy the equation as explained in the video.

### Many students have difficulty

Many students have difficulty understanding the relationship between graphs of lines and their corresponding equations. In fact, numerous studies have been conducted on this topic.

To better understand the relationship, please watch this video: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

### Hi Brent,

Hi Brent,

in the below question I am tried to solve it using the property of parallel lines (corresponding angles are equal). Thus 8x = 180-4x >>> x = 15 (one of the options) therefore making 3rd and 4th line parallel. But the answer 15. Where am I going wrong in this?

https://gmatclub.com/forum/in-the-figure-above-all-the-marked-angles-are-some-multiple-of-x-258510.html

You are assuming that which you are trying to demonstrate.

That is, we aren't told that all of the vertical lines are parallel.
In fact, it may be the case that, among the 5 vertical lines, there may be just 2 lines that are parallel. So, we can't randomly choose two lines and assume that they're parallel.

Cheers,
Brent

### And also this one - https:/

And also this one - https://gmatclub.com/forum/what-is-the-smallest-possible-distance-between-the-point-0-5-and-an-278592.html

Is the question asking the slope of the line?

Yes, once we know that the slope = -1, then we know that the line creates a 45-degree angle with the y-axis.

From there, we can create a 45-45-90 triangle by drawing a line from (0,5) that is perpendicular to the line in question.
This 45-45-90 triangle has a hypotenuse of length 2, which means the other two sides will have length √2

One of those sides (with length √2) will be the shortest distance.

Cheers,
Brent