Question

what is the equation of the line that passes through the point (-4, -4) and has a slope of 0?

Explanation:

Step1: Recall the slope - intercept form

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 the slope $m = 0$. So the equation of the line becomes $y=0\times x + b$, which simplifies to $y = b$.

Step2: Find the value of $b$

The line passes through the point $(-4,-4)$. Since the equation of the line is $y = b$, and for the point $(-4,-4)$, the $y$ - coordinate is - 4. So when $x=-4$, $y=-4$. Substituting into $y = b$, we get $b=-4$.

Step3: Write the equation of the line

Substituting $m = 0$ and $b=-4$ into the slope - intercept form $y=mx + b$, we get the equation of the line as $y=-4$.

Answer:

$y = - 4$