Question

The point slope form of the equation of the line that passes through (-5-1) and (10.-7) is
standard form of the equation for this line?

Answer 1

Answer:

The standard form of the equation for this line can be:

l: 2x + 5y = -15.

Step-by-step explanation:

Start by finding the slope of this line.

For a line that goes through the two points $(x_0, y_0)$ and $(x_1, y_1)$,

$\displaystyle \text{Slope} = \frac{y_{1} - y_{0}}{x_{1} - x_{0}}$.

For this line,

$\displaystyle \text{Slope} = \frac{(-1) - (-7)}{(-5) - 10} = -\frac{2}{5}$.

Find the slope-point form of this line's equation using

• $\displaystyle \text{Slope} = -\frac{2}{5}$, and
• The point $(-5, -1)$ (using the point $(10, -7)$ should also work.)

The slope-point form of the equation of a line

• with slope $m$ and
• point $(x_{0}, y_{0})$

should be $l:\; y - y_{0} = m(x - x_0)$.

For this line,

• $\displaystyle m = -\frac{2}{5}$, and
• $x_0 = -5$, and
• $y_0 = -1$.

The equation in slope-point form will be

$\displaystyle l:\; y - (-1) = -\frac{2}{5}(x - (-5))$.

The standard form of the equation of a line in a cartesian plane is

$l: \; ax + by = c$

where

$a$, $b$, and $c$ are integers. $a \ge 0$.

Multiply both sides of the slope-point form equation of this line by $5$:

$l:\; 5 y + 5 = -2x -10$.

Add $(2x-5)$ to both sides of the equation:

$l: \; 2x + 5y = -15$.

Therefore, the equation of this line in standard form is $l: \; 2x + 5y = -15$.