Respuesta :
Strategy 1:
There's a formula that gives the equation of a line, given two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:
[tex]\dfrac{x-x_2}{x_1-x_2}=\dfrac{y-y_2}{y_1-y_2}[/tex]
Plug your values to get
[tex]\dfrac{x-5}{-6-5}=\dfrac{y+31}{24+31}[/tex]
Which leads to
[tex]\dfrac{x-5}{-11}=\dfrac{y+31}{55}[/tex]
Multiplying both sides by 55:
[tex]-5(x-5)=y+31 \iff -5x+25=y+31 \iff y=-5x-6[/tex]
Strategy 2:
First of all, let's compute the slope
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-31-24}{5+6}=\dfrac{-55}{11}=-5[/tex]
Then, use the slope-point formula with any of the two points:
[tex]y-y_0=m(x-x_0)[/tex]
If for example we use the first point, we have
[tex]y-24=-5(x+6) \iff y = -5x-30+24 \iff y = -5x-6[/tex]
Answer:
Step-by-step explanation:
The point slope form is expressed as
y - y1 = m(x - x1)
Where
m represents slope
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
The given points are (- 6,24) and
(5, - 31)
y2 = - 31
y1 = 24
x2 = 5
x1 = - 6
Slope,m = (- 31 - 24)/(5 - - 6)
= - 55/11 = - 5
To determine the equation, we would substitute x1 = - 6, y1 = 24 and m = - 5 into the point slope form equation. It becomes
y - 24 = - 5(x - - 6)
y - 24 = - 5(x + 6)
