Question

my problem that I have Todo is to write a slope-intercept form of the equation of the line described. I am not sure on how todo it. can you help me?

Answer 1

The general form of the equation of the line is:

`y=mx+b`

where m is the slope of the line and b the y-intersect. Lines with the same slope are considered parallels between them.

You have a line which is parallel to the line y=-1/7x -1, and tha passes trough the point (2,-1).

The slope of the searched line is m=-1/7. In order to find theequation of the line, you use the following formula for the slope of a line:

`m=(y-y_0)/(x-x_0)`

where (x0,y0) is one of the points of the line. In this case you consider this point is (2,-1). You replace these values of the point and the values of the slope into the formula for the slope and you proceed as follow:

`\begin{gathered} m=(y-(-1))/(x-2)=(y+2)/(x-2) \\ -(1)/(7)=(y+2)/(x-2) \\ (-(1)/(7))(x-2)=y+2 \\ -(1)/(7)x+(2)/(7)=y+2 \\ y=-(1)/(7)x+(2)/(7)-2 \\ y=-(1)/(7)x+(2-14)/(7) \\ y=-(1)/(7)x-(12)/(7) \end{gathered}`

The previous equation, is the equation of the searched line.