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 + 1Further explanationSolving linear equation mean calculating the unknown variable from the equation.Let the linear equation : y = mx + cIf we draw the above equation on Cartesian Coordinates , it will be a straight line with :m → gradient of the line( 0 , c ) → y - interceptGradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :[tex]\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}} }[/tex]If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :[tex]\large {\boxed{y - y_1 = m ( x - x_1 )} }[/tex]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 :[tex]\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}[/tex][tex]\frac{y - 4}{-5 - 4} = \frac{x - 1}{-2 - 1}[/tex][tex]\frac{y - 4}{-9} = \frac{x - 1}{-3}[/tex][tex]\frac{y - 4}{3} = \frac{x - 1}{1}[/tex][tex]y - 4 = 3 ( x - 1 )[/tex][tex]y = 3x - 3 + 4[/tex][tex]\large {\boxed {y = 3x + 1} }[/tex]Learn moreInfinite Number of Solutions : of Equations : of Linear equations : detailsGrade: High SchoolSubject: MathematicsChapter: Linear EquationsKeywords: Linear , Equations , 1 , Variable , Line , Gradient , Point