State whether the given statement is true or false:
The slope of the line perpendicular to $5 x + 3 y + 1 = 0$ is $\frac{4}{5}$ .

True

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False

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Solution

The correct option is B False
Two lines are perpendicular only when the product of their slopes $m_{1} . m_{2} = - 1$ .
To find the slope $m_{1}$ of first line $5 x + 3 y + 1 = 0$ , we need to rewrite in the standard form $y = m x + c$
$y = - \frac{5}{3} x - \frac{1}{3}$ and we have $m_{1} = - \frac{5}{3}$
Hence, the slope of the other line is $\frac{3}{5}$ .

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