Mathematics: Determine la ecuación general de la recta que pasa por los puntos (1,4); (- 2, - 5) y grafíquela.

400Step-by-step explanation:...

Determine la ecuación general de la recta que pasa

milkshakegrande101

13.03.2022

The equation of the line that passes through the points (1 , 4) and (-2, -5) is y = 3x + 1

Further explanation

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}} }$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\large {\boxed{y - y_1 = m ( x - x_1 )} }$

Let us tackle the problem.

Let :

(1 , 4) → (x₁ , y₁)

(-2, -5) → (x₂ , y₂)

To find the straight line equation, the following formula can be used :

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

$\frac{y - 4}{-5 - 4} = \frac{x - 1}{-2 - 1}$

$\frac{y - 4}{-9} = \frac{x - 1}{-3}$

$\frac{y - 4}{3} = \frac{x - 1}{1}$

y - 4 = 3 ( x - 1 )

y = 3x - 3 + 4

$\large {\boxed {y = 3x + 1} }$

Learn moreInfinite Number of Solutions : System of Equations : System of Linear equations : Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

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