The question is: Find an equation for the line containing line segment AB. I kind of understand (slope equation, altitude, and all the formulas). I'm just not sure the steps and process of answering a question like this/ when to use certain equations. – please explain clearly. The Cartesian plane with the line segment is shown below.
Best Answer
Here is one way to do it (Of course, there are many others):
The function for a line is given by $y=-2x-2$. Note the general equation for a line: $$y=mx+b \tag{1}$$ Note that the line segment $AB$ is perpendicular to that. Let's calculate the slope of $AB$ (Let's call this $m$) using the slope of the line given. Here, $m_1$ is the slope of the line you are given $y=-2x-2$. We can evidently see that $m_1=-2$. Therefore: $$m=-\frac{1}{m_1}=\frac{1}{2}$$ We now have $m$, now substitute it into $(1)$ and evaluate $b$ using a known point you have on the line segment $AB$. In this case, you can use $A(1,0)$.
Here is more intuition about why you have to find $b$. Since you already have the slope of $AB$, what you want to do is align the function to $AB$. Try moving the slider for $b$ on the link I've attached.