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 :
[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 more
- Infinite Number of Solutions : https://brainly.com/question/5450548
- System of Equations : https://brainly.com/question/1995493
- System of Linear equations : https://brainly.com/question/3291576
Answer details
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
