A straight line passes through the points (2,4) and (-1,-5). Find the equation.?

Question

I know the answer.....but don't know the way of solving it......anyone who can do it, describe me thoroughly, please......if you can make me understand, your answer will be chosen as a best answer!!!!

Answer 1

There are 3 ways to get the equation of a line:
1. If you are given a slope and a point.
2. If you are given the length and a point.
3. If you are given two points.

Here you have case # 3, which is similar to case # 1 in approach, with an extra step.

Your plan is:
1. Find the slope from the 2 given points.
2. Then, find the equation from a slope and one of the points, as you would in case #1.

For you to accomplish this you need to know 2 things:
1. The formula for a line( y=mx+b), Where m=slope, b=constant that you have to solve for, and may equal zero.
2. The formula for slope. (m= [(y1-y2) / (x1-x2)].

So, first find the slope, by subtracting the 2 given points from each other:
change in y = 4 - (-5) = 9
change in x = 2 - (-1) = 3
slope (m) = change in y / change in x = 9/3 = 3

Now, plug this into the line formula (y=mx+b), along with any one of the points and solve for b.
So since:
y=mx+b
4 = 3(2) + b
b= -2
and the general equation for this line becomes:
y = 3x - 2

Answer 2

First you have to use the slope formula:

m = (y2 - y1) / (x2 - x1)

You have (2,4) and (-1, -5). The first set of numbers are you "1's" and the second set of numbers are your "2's". So, the 2 would be x1, and the 4 would by y1 Similarly, the -1 would be x2, and the -5 would be y2.

Think of it like this:
( 2 , 4 ) and (-1,-5)
(x1,y1) and (x2,y2)

So now you just plug in the numbers:

m = (-5 - 4) / (-1 - 2) = 9/3, which reduces to 3

So your slope is 3.

Now you use the y-intercept formula to figure out the rest of the equation:

y = mx + b

You know what m is, and you only need to use one of your paired coordinates for x and y. It doesn't matter which you use. I will use (2,4), where 2 is the x and 4 is the y.

4 = (3)(2) + b
4 = 6 + b
-6 . -6 <---------- Subtract 6 from both sides

So b = -2

Now you know that m=3 and b=-2. Now you just put those numbers into the formula and you are done!

y = mx + b

y = 3x - 2

Answer 3

First locate the slope of the line....its (a million- -7)/(3- -2) = 8/5. the element slope equation is y-y1=m(x-x1). the place m=the slope of the line. Filling interior the blanks y- -7 = 8/5(x- -2). Simplified it is y+7=8/5x+sixteen/5. The slope intercept style of a line is y=mx+b, m=the slope and b=the y intercept of the line, y and x are constants. For this you will possibly first would desire to unravel the element slope equation for the element (0,y). So replace 0 in for x and resolve for y. you will desire to get -19/5 for the y intercept. Then replace m=8/5 and b=-19/5. You get y=8/5x-19/5.

Answer 4

Slope of the line (m) is change in y-values divided by change in x values:

m = (4 - (-5)) / (2 - (-1)) = 9 / 3 = 3

Use one of the points and the equation of a line to find the intercept value (b). I will use the point (2,4), so x=2 and y=4

y = mx + b
4 = 3(2) + b
4 = 6 + b
b = -2

So the equation of your line is y = 3x - 2
You can plug in the other specified point to check this result.

Answer 5

When two points are given you need not calculate intercept unless it is asked..

equation in point slope form is

(y - y1) = m(x - x1)

x1, y1 (any one of the coordinates given) = 2, 4

slope, m = (y2 - y1)/(x2 - x1) = (-5 -4)/(-1-2) = 9/3 = 3

substituting these values
y - 4 = 3(x -2)

= y - 4 = 3x - 6

= y - 3x + 2 = 0