Question

50 points and brainliest if right no spamming
Which is an equation in point-slope form of the line that passes through the points (4, 5) and (−3, −1) ?

y+1=6/5(x+3)
y−1=6/7(x−3)
y+1=6/7(x+3)
y+3=7/6(x+1)

Answer 1

Slope of the required line = $\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Slope of the required line = $\dfrac{-1-5}{-3-4}$

   

                                           = $\dfrac{-6}{-7}$

                                            = $\dfrac{6}{7}$

We know,

y - $y_{1}$ = m(x- $x_{1}$)  { Where m is the slope }

     Substituting the given values and slope

y - ( - 1 ) = $\dfrac{6}{7}$ { x - ( - 3 ) }

y + 1 = $\dfrac{6}{7}$ ( x + 3 )

Therefore, option C is correct.

Answer 2

$\huge \bold {\mathfrak {hey}}$

✔️ Slope = y2 - y1 / x2 - x1

➡️ slope = - 1 - 5/ - 3 - 4

➡️ slope = - 6 / - 7

We know if in denominator and no numerator minus is given they will be cut.

Therefore,

Slope = 6 / 7

We know y - y1 = m(x - x1) ( m is the slope here)

Now , substitute values

➡️ y - ( - 1) = 6/7 { x - ( - 3)}

➡️ y + 1 = 6/7 ( x + 3)

Therefore option C is correct.

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➡️ OPTION C