# find equation of straight line through point A(-2,-7) and having intercepts of length 3 between straight lines 4x+3y=12 and 4x+3y=3

4x + 3y = 12 and 4x + 3y = 3 are parallel lines

Let us first find the distance between the parallel lines

$\frac{3×4-3}{\sqrt{{4}^{2}+{3}^{2}}}=\frac{9}{5}=1.8$

Let A be the angle made by the line with 4x + 3y = 3

Let m be the slope of the line

Equation of the line:

$y-\left(-7\right)=-\frac{24}{7}\left(x-\left(-2\right)\right)$
7y + 24x + 97=0

• -97
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