Question

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

Answer 1

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 more

• Infinite Number of Solutions : brainly.com/question/5450548
• System of Equations : brainly.com/question/1995493
• System of Linear equations : brainly.com/question/3291576

Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

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