State a line equation for the line that passes through (-2, 5) and (8, -8)?

Question

I am not sure if i did this right since when I plug the points in my equation, they dont come out right.
could someone explain to me what steps i should take to figure this out? thank you

Answer 1

Hi dear EvenstarAngel ;

■ Step 1
first you need to fine the slope .
its the slope formula ;
m = ( y2 - y1 ) / (x2 - 1)
if x1 = -2 , y1 = +5 , x2 = +8 & y2 = -8 so
m = ( -8 - 5 ) / (8 - (-2)) = - 13 / 10

■ Step 2
its the line formula ;
y - y1 = m ( x - x1 )
y - 5 = -(13/10) ( x - (-2))
y = -13/10x - 26/10 + 5
10 * (y = -13/10x - 26/10 + 5)
10 y = -13x - 26 + 50
13x +10y - 24 = 0

its what we are looking for .

Good Luck Darling ♣

Answer 2

First solve for slope

m = y₂- y₁/ x₂- x₁

m = 5 - (- 8) / - 2 - 8

m = 5 + 8 / - 10

m = - 13/10

Slope equals m = - 13/10

Insert the m value into the point slope form of the equation of a line formula.

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Point Slope form of the equation of a line
Formula..

P(- 2, 8)

y - y₁= m(x - x₁)

y - 5 = - 13/10[x - ( - 2)]

y - 5 = - 13/10[x + 2}

10(y - 5) = 10( - 13/10)[x + 2]

10y - 50 = - 13[x + 2]

10y - 50 = - 13x - 26

10y - 50 + 50 = - 13x - 26 + 50

10y = - 13x + 24

10y/10 = - 13/10x + 24/10

y = - 13/10x + 12/5

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Answer 3

knowing that a line equation is y=a*x + b, I can replace x and y with the known points:
5= a * (-2) + b
(-8) = a * 8 + b

From the first equation: a= (5-b)/(-2) = (b-5)/2
I can replace a in the second equation:
(-8) = (b-5)*8/2 + b
(-8) = 4*b -20 + b = 5*b -20
b= (-8+20) / 5 = 12/5
I can now replace b in the equation above to find a:
a= (12/5 -5 ) /2 = 12/10 - 5/2 = (12-25)/10 = -13/10
The line equation is
y= -13/10*x + 12/5 = -1,3*x + 2,4

Answer 4

y=mx+b is the line equation form.
m stands for slope and y stands for y-intercept.

1. Find the slope (m) by the equation (y2-y1)/(x2-x1). So that is (-8-5) /(8- -2)= -13/10= -1.3<-- This is the slope. You can use the decimal -1.3 or the fraction -13/10 for the slope.
2. Next, find the y-intercept (b). So far, you have the equation of y=-1.3x+b. Plug in one of the points: either (-2,5) or (8, -8). Let's pluf in (-2,5) in the equation. So, it's 5= -1.3(-2)+b. Let's simplify it:
5=2.6+b
2.4=b
Now, the y-intercept is 2.4
3. Now you have the equation of the line that passes through (-2,5) and (8,-8) which is y= -1.3x+2.4 or you can make it into another equation, 1.3x+y=2.4

You may check my equation by plugging in the points.

Answer 5

(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
is the formula give two points
plugging in
(y-5)/(-8-5)=(x--2)/(8--2)
10(y-5)=-13(x+2)
10y-50=-13x-26
13x+10y-24=0

Answer 6

m=(y2-y1)/(x2-x1)
(-8-5)/(8+2)
-13/10

y-y1=m(x-x1)
y-5=-13/10(x+2)
y-5=-13/10x-26/10
y=-13/10x-26/10+50/10
y=-13/10x+12/5

Check:
5=-13/10(-2)+12/5
5=13/5+12/5
5=25/5
5=5

-8=-13/10(8)+12/5
-8=-52/5+12/5
-8=-40/5
-8=-8

I hope this helps!

Answer 7

(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
(y-5)/(-8-5)=(x--2)/(8--2)
10(y-5)=-13(x+2)
10y-50=-13x-26
13x+10y-24=0