An equation of the line through the points (−2,5) and (3,−4) is

Question

Its hard for me to solve help please

 

Answer 1

The equation you'll probably use most often to describe any line is  y=mx+b, where Y and X are the coordinates of any given point on the line, M is the line's slope, and B  is the y-intercept. (Hence the name of this formula, "slope-intercept form.")

 

You already know, not one, but two sets of x- and y- coordinates: (-2,5) and (3,-4). What you don't know yet are the slope and the y-intercept of the line intersecting them. 

We'll start with slope, often described as "rise over run." This just means you calculate it by dividing the vertical change on the y-axis ("rise") by the horizontal change on the x-axis ("run"). To get from point (-2,5) to (3,-4), you'll have a "rise" of -9 units (the difference between your y coordinates) and a "run" of 5 units (the difference between your x coordinates). Rise/run = slope = -9/5.

If we plug that into the slope-intercept formula, we get y=(-9/5)x+b. Remember that we also have, not one, but two sets of x- and y- coordinates, which can be plugged right back into this formula. If we try it with the first set, (-2,5), the equation of our line becomes 5=(-9/5)*(-2)+b.

 

Since there's only one variable left, we can now solve for b:
5=(-9/5)*(-2)+b
5=(18/5)+b

5-(18/5)=b
(25/5)-(18/5)=b
7/5=b

Now we have our y-intercept to plug into the equation, which becomes: 5=(-9/5)*(-2)+(7/5).

To check that it works for more than just that ordered pair, swap in the second pair of coordinates  we were given, (3,-4), but leave the slope and y-intercept values unchanged. The equation becomes -4=(-9/5)*(3)+(7/5). But is that true?

 

Solve:
-4=(-9/5)*(3)+(7/5)
-4=(-27/5)+(7/5)
-4=(-20/5)
-4=-4

The equation is true! Now we know that the slope and y-intercept values will work for any ordered pair of coordinates on that line. So, the equation defining the line is:

 

y=(-9/5)x+(7/5)

Answer 2

Hi Jvon, using the two points, you need to find the slope of the line. The slope is given by:

 

m (represents the slope) = (y₂ - y₁) / (x₂ - x₁)

 

It does not matter which point is used as point one, the results is the same.

 

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

 

m = -9 / 5

 

Use the point-slope form of the line to find the line. Again, it does not matter which of the two points you use.

 

y - y₁ = m * (x - x₁)

 

y - 5 = -9/5 * (x - (-2))

 

y - 5 = -9/5 * (x + 2)

 

Multiply entire equation by 5 to clear the fraction:

 

5y - 25 = -9 * (x + 2)

 

5y - 25 = -9x - 18

 

Put into standard form, Ax + By = C:

 

9x + 5y = 7

 

Questions?

Answer 3

First, find the slope.

 

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

 

Now, plug in either point.

 

y - 5 = (-9/5)(x - (-2))

y - 5 = (-9/5)x - 18/5

y = (-9/5)x + 7/5