Question

Write an equation of a line that passes through (-1,-3) and is parallel to 4x+5y=6

Answer 1

First let's find the slope of the given line

`\begin{gathered} 4x+5y=6 \\ 5y=-4x+6 \\ y=(-4)/(5)x+6 \\ so\text{ by slope intercept form , slope of given line is }(-4)/(5) \end{gathered}`

Since the rerquired line is parallel to the given line so its slope will also be -4/5 as slope of two parallel lines is same.

Now let's find the equation of the required line by point-slope form :-

`\begin{gathered} y-(-3)=(-4)/(5)(x-(-1)) \\ y+3=(-4)/(5)((x+1)) \\ 5y+15=-4x-4 \\ 4x+5y=-19 \end{gathered}`

So the equation of the requird line is 4x+5y=-19