Math question! please help?

Question

what is the equation of the line that contains the points with (x,y) coordinates (-3,7) and (5,-1).......

Answer 1

Your general equation is
y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point.
m = (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two points on the line.
m = (-1-7)/(5-(-3)) = -8/8 = -1
y - 7 = -1(x+3)
y - 7 = -x - 3
y = -x + 4

Answer 2

Since the slope of a line is given by
m = slope
m = rise/run = change in y(vertical)/change in x(horizontal) = ∆y/∆x
m = ∆y/∆x

If the line passes through points with coordinates (x1,y1) and (x2,y2),
Let
∆y = y2 - y1
∆x = x2 - x1

Substitute these into m
m = (y2 - y1)/(x2 - x1) and you get the slope formula


If the line passes through point with coordinates (x1,y1) and in general through the point (x,y). Let
∆y = y - y1
∆x = x - x1

Substitute these into m
m = (y - y1)/(x - x1)
m(x - x1) = (y - y1)
y - y1 = m(x - x1) and you get the point-slope formula

Since the coordinates are (-3,7) and (5,-1). The slope is determined by
∆y = (-1) - (7) = -1 - 7 = -8
∆x = (5) - (-3) = 5 + 3 = 8
m = ∆y/∆x = -8/8 = -1

Therefore the slope is 1. If we let x1 = -3 and y1 = 7 (including the slope m = -1) then substitute these into the "point-slope formula",
y - y1 = m(x - x1)
y - (7) = (-1)[x - (-3)]
y - 7 = -(x + 3)
y - 7 = -x - 3
y - 7 + x + 3 = 0
x + y - 4 = 0 or x + y = 4 or y = -x + 4

Therefore, the equation of the line that contains the points (-3,7) and (5,-1) is
x + y - 4 = 0 (General form)
or
x + y = 4 (Standard form)
or
y = -x + 4 (slope-intercept form)

^_^

I have another tip for you:
Let
(-3,7) correspond to (x1,y1) and
(5,-1) correspond to (x2,y2)

Since we have 2 equations
m = (y2 - y1)/(x2 - x1) and
y - y1 = m(x - x1)

Substitute m into the second equation
y - y1 = (y2 - y1)/(x2 - x1) · (x - x1)

Multiply (x2 - x1) to both sides and simplify
x2 y - x1 y - x2 y1 + x1 y1 = y2 x - y1 x - x1 y2 + x1 y1

Subtract x1 y1 from both sides
x2 y - x1 y - x2 y1 = y2 x - y1 x - x1 y2

Transpose - x2 y1 to the other side
x2 y - x1 y = y2 x - y1 x - x1 y2 + x2 y1

Transpose all x's to the right and factor
(x2 - x1)y - (y2 - y1)x = -(x1 y2 - x2 y1)

Multiply -1 to both sides
(y2 - y1)x + (x1 - x2)y = x1 y2 - x2 y1

Since
(-3,7) --> (x1,y1) and
(5,-1) --> (x2,y2),
x1 = -3
x2 = 5
y1 = 7
y2 = -1
and
(y2 - y1)x + (x1 - x2)y = x1 y2 - x2 y1
(-1 - 7)x + (-3 - 5)y = (-3)(-1) - (5)(7)
(-8)x + (-8)y = 3 - 35
(-8)x + (-8)y = -32
(-8)x + (-8)y = (-8)4
Divide by (-8),
x + y = 4

^_^

Answer 3

A linear equation is of the form

y= m x + b

where m is the slope. Slope is defined as the change in y divided by the change in x.

Here your points are (-3,7) and (5,-1) so the change in x is 8 when the change in y is -8. So m is -1

y = -x + b

Now we need to find b, We can simply put the value of one x and the corresponding y in there:

7 = 3 + b

so b is 4.

Equation is y = -x + 4

Answer 4

there are several ways to do this but they all come from the same principles

start with the slope/intercept form of the equation of a line
y=mx+b
insert each x,y coordinate in the line equation
7=m(-3)+b
5=m(-1)+b
now you have two equations and two unknowns that you can solve, I would solve by subtracting the second equation from the first to get
2=-2m
-1=m
so, we have the slope, m, and we can substitue the value for m in either equation
7=(-1)(-3)+b
7=3+b
4=b

hooray
that makes the equation
y=-x+4

a quick check of the points 7=(-3)(-1)+4 yep and 5=(-1)(-1)+4 yep again

excellent

keep at it

Answer 5

Let y=ax+b
using the coordinates (-3,7) and (5,-7)
-3and 5 are the x coordinates, so we put them in the "x" place in "y=ax+b"
7and -1 are the y coordinates, so we put them in the "y" place in "y=ax+b"
then it will form a linear equation.
7= -3a+b------------1
-1=5a+b-------------2
use the second equation to minus the first one
and we get
8a= -8
so a= -1
and b will equal 4
so y= -x+4




THE ANSWER IS
y= -x+4

Answer 6

find the slope:
m = (-1-7)/(5--3) = -1

then the equation is:
y= -x+b, where b= y-intercept

use one point:
7 = -(-3)+b
b = 4

the equation is:
y = -x + 4

sometimes placed in standard form:
x + y = 4 or x + y - 4 = 0

Answer 7

slope:
m = (-1-7)/(5--3) = -1

then equation is:
y= -x+b, ( b is y-intercept)

use one point:
7 = -(-3)+b
b = 4

the equation is:
y = -x + 4

sometimes placed in standard form:
x + y = 4 or x + y - 4 = 0

Answer 8

Use the two-point formula:

y - y1 = [(y2 - y1)/(x2 - X1)](x - x1)

y - 7 = [(-1 - 7)/(5 - (-3))](x - (-3))

y - 7 = (-8/8)(x + 3)

y - 7 = -x - 3

y = -x + 4

Therefore:

x + y = 4

Answer 9

(-3,7) and (5,-1)

m = (-1 - 7)/(5 - (-3))
m = (-1 + (-7))/(5 + 3)
m = (-8)/8
m = -1

(-3,7), m = -1
7 = -1(-3) + b
7 = 3 + b
b = 4

ANS : y = -x + 4

Answer 10

I believe you need to use the y=mx+b and m=slope=(y1-y2)/(x1-x2)
then you use the x and y coordiantes to find b. then you just plug the m and b in eq. I believe the eq is Y=4x+19