Question

what is the equation in point-slope form for the line parallel to y=3x+2 that contains P(-7,-6)? PLEASE HELP

Answer 1

point slope form.. do you know

Answer 2

y-y1=m(x-x1)

Answer 3

I dont know how to do it can u help

Answer 4

The general equation in point slope form is
y=mx+b
where m=slope,
b=y-intercept.
If the given line is parallel to y=3x+2 there are two ways to go about it.

\(\color{purple}{Method~~ 1:}\)
Find the slope of the line, then use the point-slope form to let the line pass through the given point.
From y=3x+2, compare with the general equation y=mx+b, we conclude that the slope is m=3.
Now substitute m=3, and point (-7,-6) as (x0,y0). follow the following point-slope example to get the equation.

\(\color{red}{Example:}\)
Find equation of the line with slope 2.5 passing through the point (4,3)
\(\color{teal}{m} = \color{teal}{2.5}\)
\((\color{blue}{x_0},\color{purple}{y_0})=(\color{blue}{4},\color{purple}{3})\)
\(Line: (y-\color{purple}{3}) = \color{teal}{2.5} (x-\color{blue}{4}) => y-\color{purple}{3}=\color{teal}{2.5}x-10 => y = 2.5x-7\)

\(\color{purple}{Method~~ 2:}\)
If a parallel line is already given, say y=\(\color{red}{m}\)x+b, and it has to pass through (\(\color{blue}{x0}\),\(\color{green}{y0}\)),
the required line is then \(y-\color{green}{y0}=\color{red}{m}(x-\color{blue}{x0})\)