Question

A line passes through (2, –1) and (8, 4).Write an equation for the line in point-slope form.

Answer 1

Answer: Equation of line in point slope form,

$y + 1 = 5 ( x - 2 )$

And, Equation of line in standard form,

$5 x - 6 y = 16$

Step-by-step explanation:

Since, If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ ,

Then the equation of line,

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

Here $x_1 = 2$, $y_1=-1$, $x_2=8$ and $y_2=4$

Thus, the equation of the given line,

$y-(-1)=\frac{4-(-1)}{8-2} (x-2)$

⇒ $y+1=\frac{4+1}{8-2} (x-2)$

⇒ $y+1=\frac{5}{6} (x-2)$ -----(1)

⇒  $6(y+1)= 5(x-2)$

⇒ 6 y + 6 = 5 x - 10

⇒ 6 = 5x - 6y - 10 ( By subtracting by on both sides )

⇒ 6 + 10 = 5x - 6y  ( By adding 10 on both sides )

⇒ 16 = 5x - 6y

⇒ 5 x - 6 y = 16 ------(2)

Since, in slope for of a line is, $y-y_1= m (x-x_1)$

Thus, equation (1) shows the in slope form of the line.

And, standard form of the line is ax + by = c where a, b and c are the integers.

Thus, equation (2) shows the standard form of the given line.

Answer 2

Hello : let  A(2,-1)    B(8,4)
the slope is :   (YB - YA)/(XB -XA)
(4+1)/(8-2)  = 5/6

an equation for the line in point-slope form is : y-(-1) =( 5/6)(x-2)
y+1 = (5/6)x -5/3
6y+6 = 5x -10
the equation in standard form is : 5x-6y = 16