Lesson: Writing Equations

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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
gmat-admin's picture

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 why coordinates will satisfy the equation as explained in the video.
gmat-admin's picture

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...

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