Write the equation in standard form for the line that crosses the two points. (-7,9), (-10,11)

Question

I just really struggle with these types of questions. I always get confused on what it is I have to do first and which numbers I can put where without messing the whole problem up. Can someone please show me and explain what it is that I have to do while making it easy for me to understand at the same time?

Answer 1

(-7,9) (-10,11)

First find the slope = "rise over run" the change in y coordinates divided by the corresponding change in x coordinates = (11-9)/(-10- -7) = 2/(-10+7) = 2/-3 = -2/3

general formual for a standard linear equation in slope intercept form is

y = mx + b where m= slope and b = y intercept

y= (-2/3)x + b. To solve for b plug in either point

9 = (-2/3)(-7) + b

b = 9-14/3 = 27/3 - 14/3 = 13/3

y = (-2/3)x + 13/3 is the equation through the two given points

that's standard form for slope intercept form, but "standard form" might also mean ax+by = c type form

IF so, eliminate the fractions, multiply by 3

3y =-2x +13, move the x term to the left side

2x +3y = 13 which is in ax+by=c form with a=2, b=3 and c=13

Another "standard form" is the point slope form

That might also be what is meant in this problem

use either point

y-9 = (-2/3)(x+7)

or

y-11 = (-2/3)(x+10)

they're all equivalent equations for the line through the two points

Personally, without more information, I'd go with 2x+3y = 13. It avoids fractions and negative signs. It just looks "cleaner," simpler, less complicated.