SOLUTION: I am supposed to write an equation in standard form of the line passing through these points. (1,-1) and (5,6). PLEASE HELP!!!!!! The answer is -7x+4y=-11, but I don't know how to

Question 128025This question is from textbook algebra: structure and method: book1
: I am supposed to write an equation in standard form of the line passing through these points. (1,-1) and (5,6). PLEASE HELP!!!!!! The answer is -7x+4y=-11, but I don't know how to get there. HELP MUCH APPRECIATED!!!! This question is from textbook algebra: structure and method: book1

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You are given (,) and (,). Which point you assign the designation and which you assign doesn't make any difference as long as you keep it consistent as you work the problem.

So lets say is (,) and is (,).

That means:

The equation for a line through two points is given by:

Just substitute the numbers:

And do the arithmetic:

Now we need to put the equation into standard form. Standard form is

Multiply both sides by 4:

Distribute and remove parentheses:

Add -7x to both sides:

Add -4 to both sides:

Actually that is good enough, but I would multiply both sides by -1, just because it is neater.

Ah yes, Monk would approve.

Check the answer:
If the line represented by the derived equation actually passes through the two given points, each of the sets of given x- and y-coordinates will make the equation a true statement when substituted.

So. , so the first point makes the equation true. And , so the second point makes the equation true. Answer checks.
RELATED QUESTIONS
I am supposed to write an equation in standard form of the line passing through these... (answered by stanbon)

Write an equation in standard form of the line passing through the points (-4/9,4/9) and... (answered by josgarithmetic)

I just do not know how to do these. Please help? Write the equation of the line passing... (answered by stanbon)

I am having a dog of a time trying to solve these problems, please help me. Write the... (answered by scott8148)

Write an equation in standard form of the line passing through the points (5,3) and... (answered by josgarithmetic,Boreal)

Find the slope of a line perpendicular to the line y=x Use the... (answered by Alan3354)

Write in standard form an equation of the line passing through the given point with the... (answered by jim_thompson5910)

Write an equation in standard form for a line passing through the pair of points (0,6) (answered by elima)

Write an equation in standard form for a line passing through the pair of points.... (answered by stanbon)