Question

find the point slope equation for the line that passes through the points (-6,24)and (5,-31) use the first point in your equation

Answer 1

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)

Answer 2

Strategy 1:

There's a formula that gives the equation of a line, given two points $(x_1,y_1)$ and $(x_2,y_2)$:

$\dfrac{x-x_2}{x_1-x_2}=\dfrac{y-y_2}{y_1-y_2}$

Plug your values to get

$\dfrac{x-5}{-6-5}=\dfrac{y+31}{24+31}$

Which leads to

$\dfrac{x-5}{-11}=\dfrac{y+31}{55}$

Multiplying both sides by 55:

$-5(x-5)=y+31 \iff -5x+25=y+31 \iff y=-5x-6$

Strategy 2:

First of all, let's compute the slope

$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-31-24}{5+6}=\dfrac{-55}{11}=-5$

Then, use the slope-point formula with any of the two points:

$y-y_0=m(x-x_0)$

If for example we use the first point, we have

$y-24=-5(x+6) \iff y = -5x-30+24 \iff y = -5x-6$