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

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

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 :

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

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 :

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

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

15 units use socratic

step-by-step explanation: 15 units

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.