Question : The equation of the line if its slope is $-\frac{3}{7}$ and it passes through the point (5, 2) is:
Option 1: $3x+7y=29$
Option 2: $3x-7y=1$
Option 3: $3x+7y=1$
Option 4: $3x-7y=29$
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Correct Answer: $3x+7y=29$
Solution :
To find: Equation of the line with slope $-\frac{3}{7}$that passes through the point (5, 2).
The equation of a line passing through $(x, y)$ is $y=mx+c$, where $m$ is the slope and $c$ is the y-intercept.
Here, $m=-\frac{3}{7}$ and $(x, y)=(5,2)$
$⇒ 2=-\frac{3}{7}×5+c$
$⇒ c=\frac{15}{7}+2$
$⇒ c=\frac{29}{7}$
By putting these values in the equation of the line, $y=mx+c$
$⇒ y=-\frac{3}{7}×x+\frac{29}{7}$
$⇒ 3x+7y=29$
Hence, the correct answer is $3x+7y=29$.
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