a line passes through the points (-14, -6) and (6, -6). write its equation in slope - intercept form. write…

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(-14,-6)$ and $(x_2,y_2)=(6,-6)$. So, $m=\frac{-6-(-6)}{6 - (-14)}=\frac{-6 + 6}{6+14}=\frac{0}{20}=0$.

Step2: Find the y - intercept

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use either of the two given points. Let's use $(6,-6)$. Substitute $x = 6$, $y=-6$ and $m = 0$ into $y=mx + b$. We get $-6=0\times6 + b$, so $b=-6$.

Step3: Write the equation

Substitute $m = 0$ and $b=-6$ into $y=mx + b$. The equation of the line is $y=0x-6$, which simplifies to $y=-6$.

Answer:

$y=-6$