How to write the slope-intercept form of the equation of a line described (– 2, – 1) parallel to \[y=\dfrac{-3}{2}x-1?\]

Hint: We are asked to find the slope-intercept form of the line which is parallel to \[y=\dfrac{-3}{2}x-1\] and it also passes by (– 2, – 1). To solve this we will first understand what slope-intercept form of the line is and then how we can use the line parallel to the given line to solve our problem. We will use the slope-intercept form of a line as y = mx + c where m is the slope and c is the intercept.

Complete step by step answer:
We are asked to find the slope-intercept form of a line that is parallel to \[y=\dfrac{-3}{2}x-1\] and is passing through (– 2, – 1). Before we find the slope solution, we will see what slope-intercept is. The slope-intercept form of a line means the equation of the line which is formed using the slope and the intercept. It is given as y = mx + c where m is the slope and c is the intercept.
Now, remember we know that when two lines are parallel to each other then it means their slopes are always equal. So, it means the slope of our required line is the same as the slope of the line \[y=\dfrac{-3}{2}x-1.\]
Now, we will reduce the line in the slope-intercept form to get the slope. If we look closely at \[y=\dfrac{-3}{2}x-1\] we can see it is already in slope-intercept form. So, comparing it with y = mx + c, we get, \[m=\dfrac{-3}{2}\] and hence it means its slope is \[\dfrac{-3}{2}.\] So, the slope of our equation is \[\dfrac{-3}{2}.\] Now our equation becomes \[y=\dfrac{-3}{2}x+c.\] Now as our line passes by (– 2, – 1), so we put x = – 2 and y = – 1 and solve for c. So, putting the above values, we get,
\[\Rightarrow -1=\dfrac{-3}{2}\times \left( -2 \right)+c\]
On simplifying, we get,
\[\Rightarrow -1=3+c\]
Subtracting 3 on both the sides, we get,
\[\Rightarrow c=-1-3\]
\[\Rightarrow c=-4\]
So, c = – 4.

Hence, we get our equation as \[y=\dfrac{-3}{2}x-4.\]

Note: While we solve the equation we should be careful on solving the term that includes brackets. When we have the term inside the bracket and we have to multiply that with some term, so error happens like a (b + c) = ab + c, we may miss calculating the product with each term. Also, y – intercept is defined as the point on the y – axis where the given line cuts the y – axis. If y – intercept is 4, it means the line cuts y – axis at 4 and x – intercept means the point where the graph cut at x – axis.