You can put this solution on YOUR website!
Let's first identify your points:
That means that
Step 1: Find the slope:
The slope is given by
Just substitute the coordinate values:
Two point form:
But notice that the big fraction on the right side of the two-point form is the same as the slope calculation, which allows us to write the point-slope form:
Substituting, remembering that we said
in step 1:
Note that once you simplify the big fraction in the two-point form, the two-point and point-slope forms give you identical equations.
Step 3: Solve for y.
Add 5 to both sides:
Check the answer: If we did this correctly, the x- and y-coordinates of the given points, when substituted into the equation for x and y, will make the equation a true statement.
Both true, answer checks.
Do the rest of your problems the same way. Hint: Be extremely cautious with signed numbers. Another hint: Check your work for every problem. If an answer doesn't check, the odds are good that you made a sign error. Good luck.
Super-Double-Plus-Extra Credit. What would have happened if I had identified the points the opposite way in the beginning of this problem, that is, if I had said (1,5) is
and (2,7) is
? Would I have gotten the same or different results at the end?