What is an equation of the line that passes through the points (5, 5) and (-5, -7))?

This is a problem of 2 equations with 2 unknowns.

A general equation of a line is y = mx + b, and in this case the unknowns I refer to are m and b.

Since 2 points on the line are given, I can plug one of those into the equation to come up with an equation in 1 unknown; then use the 2nd point to determine the last unknown.

So…using (5,2), 2 = 5m + b or b = 2 - 5m.

Now, using this value for b, I use the 2nd point (-5,7), as follows:

7 = -5m + 2 - 5m or -10m = 5, so…m = -1/2

If b = 2 - 5m, then b = 4 1/2

So the equation of the line Vikas is looking for is:

y = -1/2 x + 4 1/2

Step-by-step explanation: