Question

Line p passes through A(-2, -4) and has a slope of 1/2. What is the standard form of the equation for line p?

Answer 1

Answer:

The standard form of the equation of the line is $-x +2\cdot y = -10$.

Explanation:

From Analytical Geometry, we find that the standard form of the equation of the line is:

$A\cdot x + B\cdot y = C$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

Besides, a line can be defined by the following formula:

$y = m\cdot x + b$ (2)

Where:

$m$ - Slope.

$b$ - Intercept.

By direct comparison, we find the following relationships:

$B\cdot y = -A\cdot x + C$

$y = -\frac{A}{B} \cdot x + \frac{C}{B}$

$m = - \frac{A}{B}$ (3)

$b = \frac{C}{B}$ (4)

If we know that $(x,y) = (-2,-4)$ and $m = \frac{1}{2}$, then the intercept of the equation is:

$b = y-m\cdot x$

$b = -4+\left(\frac{1}{2} \right)\cdot (-2)$

$b = -5$

If $B = 2$, then $A = -1$ and $C = -10$, and the standard form of the equation is:

$-x +2\cdot y = -10$ (5)