Answer:
The standard form of the equation of the line is [tex]-x +2\cdot y = -10[/tex].
Explanation:
From Analytical Geometry, we find that the standard form of the equation of the line is:
[tex]A\cdot x + B\cdot y = C[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
Besides, a line can be defined by the following formula:
[tex]y = m\cdot x + b[/tex] (2)
Where:
[tex]m[/tex] - Slope.
[tex]b[/tex] - Intercept.
By direct comparison, we find the following relationships:
[tex]B\cdot y = -A\cdot x + C[/tex]
[tex]y = -\frac{A}{B} \cdot x + \frac{C}{B}[/tex]
[tex]m = - \frac{A}{B}[/tex] (3)
[tex]b = \frac{C}{B}[/tex] (4)
If we know that [tex](x,y) = (-2,-4)[/tex] and [tex]m = \frac{1}{2}[/tex], then the intercept of the equation is:
[tex]b = y-m\cdot x[/tex]
[tex]b = -4+\left(\frac{1}{2} \right)\cdot (-2)[/tex]
[tex]b = -5[/tex]
If [tex]B = 2[/tex], then [tex]A = -1[/tex] and [tex]C = -10[/tex], and the standard form of the equation is:
[tex]-x +2\cdot y = -10[/tex] (5)
