SOLUTION: Write an equation of the line that passes through the pair of points. (−2, −3), (4, 5)

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line that passes through the pair of points. (−2, −3), (4, 5)      Log On


   

Question 1204563: Write an equation of the line that passes through the pair of points.
(−2, −3), (4, 5)
Found 4 solutions by josgarithmetic, mananth, greenestamps, ikleyn:
Answer by josgarithmetic(39732) About Me  (Show Source):
You can put this solution on YOUR website!
Too routine, and instructional textbooks for the examples are plentiful. Too many of these examples have already been solved at www . algebra . com

Here is any of them in general.
Points on a line, (p,v) and (h,k)

Using point-slope form
%28y-k%29%2F%28x-h%29=%28v-k%29%2F%28p-h%29
y-k=%28%28v-k%29%2F%28p-h%29%29%28x-h%29
y=%28%28v-k%29%2F%28p-h%29%29%28x-h%29%2Bk----------which on its way but not quite slope-intercept form, if that were what
you wanted. You would substitute your given values and simplify. You would want to correspond
with y=mx+b.

Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation of the line that passes through the pair of points.
(−2, −3), (4, 5)
Write an equation of the line that passes through the pair of points.
Let P (−2, −3)(x1,y1) and ,Q (4, 5),(x2,y2)
The equation of line passing through two points is
%28%28x-x1%29%2F%28x1-x2%29%29=+%28%28y-y1%29%2F%28y1-y2%29%29
plug the values



%28x%2B2%29%2F-6=+%28y%2B3%29%2F-8
simplify
-8(x+2)=-6(y+3)
-8x-16=-6y-18
-8x+6y+2=0
8x-6y-2=0







Answer by greenestamps(13295) About Me  (Show Source):
You can put this solution on YOUR website!


The responses from both of the other tutors say to plug numbers into a formula that gives you the equation of a line passing through two given points.

If you are in a job where you have to do that 50 times a day, then having a formula to plug numbers into is useful.

But plugging numbers into a formula doesn't teach you much. And what if you are a beginning student and are not familiar with the formula and accidentally plug the numbers in the wrong places?

Assuming you are a student just starting to learn algebra, it is best if you work the problem using basic ideas.

To find the slope of the line, I strongly recommend using "rise over run" with a mental (or paper and pencil) sketch of the given points -- instead of using the ubiquitous formula for calculating the slope.

The run (change in x) is 6, from -2 to 4; the rise is 8, from -3 to 5. So the slope "rise over run" is 8/6 or 4/3.

Then I think the most instructional way to find the equation is to use the slope-intercept form of the equation with one of the given points to find the intercept. Using (x,y)=(4,5):

y=mx%2Bb
5=%284%2F3%29%284%29%2Bb
5=16%2F3%2Bb
b=-1%2F3

One form of the equation is then

y=%284%2F3%29x-1%2F3

You can of course write the equation in equivalent forms. Multiplying by 3 to clear the fractions...

3y=4x-1
4x-3y-1=0
4x-3y=1

Answer by ikleyn(53614) About Me  (Show Source):
You can put this solution on YOUR website!
.

Hello a reader,

Be informed and keep in your mind that the picture in the post by @mananth does not correspond
to the equation derived by @mananth and contradicts to it !

Indeed, this line in the plot does not pass through the given points !

The true line, which corresponds to the derived equation, must go "from left lower part of the screen to right upper part".