Question

Determine the equation of the line that goes through the points (-8, -1) and (4,-10)

Answer 1

Answer:

To determine the equation of a straight line with 2 coordinates, we use the Two Point Form method.

According to the two point form method,

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

where,

• x₁, x₂, y₁, y₂ are the respective values of the two points given.
• x, y are variables for determining the equation.

According to the question,

x₁ = -8, y₁ = -1

x₂ = 4, y₂ = -10

Substituting the values we get:

$\implies \dfrac{x-(-8)}{y-(-1)} = \dfrac{4 - (-8)}{-10 -(-1)}\\\\\\\implies \dfrac{(x+8)}{(y+1)} = \dfrac{4+8}{-10+1}\\\\\\\implies \dfrac{(x+8)}{(y+1)} = \dfrac{12}{-9}\\\\\\\text{Cross multiplying we get:}\\\\\implies -9(x+8) = 12(y+1)\\\\\implies -9x -72 = 12y + 12\\\\\implies 9x + 12y + 72 + 12 = 0\\\\\implies \boxed{ \bf{9x + 12y + 84 = 0}}$

Hence the equation of the line passing through the points (-8,-1) and (4,-10) is 9x + 12y + 84 = 0.

Answer 2

Answer:

$\: \: \: \: \: \: \: \: \large \green {\boxed{ \sf 3x + 4y + 28 = 0} } \:$

Explanation :

Method :

To determine the equation of a straight line with 2 coordinates, which are $(x_1\:,\:y_1)$ and $(x_2\:,\:y_2)$ then the equation which is passing through those points :

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

Here, x and y are variables for determining the equation.

According to the question,

here is two poins which are (-8,-1) and (4,-10)

so,

$x_1 = - 8 \\ x_2 = 4 \\ y_1 = - 1 \\ y_2 = - 10$

Now, our equation is :

$\sf \: \: \: \: \: \frac{x - ( - 8)}{ - 8 - 4} = \frac{y - ( - 1)}{ - 1 - ( - 10)} \\ \sf \implies \: \frac{x + 8}{ - 12} = \frac{y + 1}{9} \\ \sf \implies \: 9(x + 8) = - 12(y + 1) \\ \sf \implies \: 9x + 72 = - 12y - 12 \\ \sf \implies \: 9x + 12y + 72 + 12 = 0 \\ \sf \implies \: 9x + 12y + 84 = 0 \\ \sf \implies \: 3x + 4y + 28 = 0 \: \: \: \: \{ \sf \:both\:side\:are\: divided \: by \: 3 \} \\ \\ \: \: \: \: \: \: \: \: \large \green {\boxed{ \sf 3x + 4y + 28 = 0} }$