Answer:
The equation of the line is 3x + 4y + 12 = 0
Step-by-step explanation:
[tex]given \: that \: the \: line \: passes \: through \: (4 , - 6) \\ and \: has \: the \: slope \: of \: \frac{ - 3}{4} \\ the \: equation \: of \: the \: line \: is \\ y - y1 = m(x - x1) \\ here \: x1 = 4 \: \: \: y1 = - 6 \: \: and \: m = \frac{ - 3}{4} \\ on \: substituting \: the \: values \: in \: formula \\ y - ( - 6) = \frac{ - 3}{4} (x - 4) \\ y + 6 = \frac{ - 3}{4} (x - 4) \\ 4(y + 6) = - 3(x - 4) \\ 4y + 24 = - 3x + 12 \\ 3x + 4y + 24 - 12 = 0 \\ 3x + 4y + 12 = 0[/tex]
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