Answer:
Step-by-step explanation:
The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9
To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.
= (1 / determinant of A) x Adjoint of A
the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2
Adjoint of A =
=
=
We have to determine the equation of the line passing through the point (2,-5) and parallel to the line
When two lines are parallel, then the slopes of the two lines are equal.
Equation of line with point and slope 'm' is given by:
Since, we have to determine the equation of a line with point (2,-5).
So, the equation of the line is :
Since, the line is parallel to the line
So,
So, slope of the line 'm' is .
Therefore, the equation of the line is:
Therefore, is the required equation of the line.
Answer:
y = - x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = =
= -
Since the line crosses the y- axis at (0, 6) ⇒ b = 6
y = - x + 6 ← equation of line
