escribir la ecuación de la siguiente recta.

Explanation:

Step1: Identify two - points

The line passes through points $(0,2)$ and $(-1,- 4)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(-1,-4)$. Then $m=\frac{-4 - 2}{-1-0}=\frac{-6}{-1}=6$.

Step3: Use the slope - intercept form $y = mx + b$

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m = 6$ and from the point $(0,2)$, when $x = 0$, $y=2$, so $b = 2$.

Step4: Write the equation of the line

Substitute $m = 6$ and $b = 2$ into $y=mx + b$, we get $y=6x + 2$.

Answer:

$y = 6x+2$