The x - and y - coordinates of point P are ( - 1 , 2 )
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.
Given:
P is ⅔ the length of the line segment from A to B.
Let:
m = 2
m + n = 3
A(9 , -8) → x₁ = 9 , y₁ = -8
B(-6 , 7 ) → x₂ = -6 , y₂ = 7
We can use the formula that is already available in the problem.
[tex]x = (\frac{m}{m+n})(x_2 - x_1) + x_1[/tex]
[tex]x = (\frac{2}{3})(-6 - 9) + 9[/tex]
[tex]x = (\frac{2}{3})(-15) + 9[/tex]
[tex]x = 2(-5) + 9[/tex]
[tex]x = -10 + 9[/tex]
[tex]\boxed {x = -1}[/tex]
[tex]y = (\frac{m}{m+n})(y_2 - y_1) + y_1[/tex]
[tex]y = (\frac{2}{3})(7 - (-8)) + (-8)[/tex]
[tex]y = (\frac{2}{3})(15) - 8[/tex]
[tex]y = 2(5) - 8[/tex]
[tex]y = 10 - 8[/tex]
[tex]\boxed {y = 2}[/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
