Find the equation of the straight line which has y-intercept equa… - Vidyadip

Question

Find the equation of the straight line which has y-intercept equal to $\frac{4}{3}$ and is perpendicular to 3x - 4y + 11 = 0.

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Answer

Any line having y-intercept equal to $\frac{4}{3}$ passes through the point $\Big(0,\frac{4}{3}\Big)\$\text{x}_1,\text{y}_1)$ Slope of line 3x - 4y + 11 = 0 $\text{y}=\frac{3}{4}\text{x}+\frac{11}{4}$ $\Rightarrow\text{m}=\frac{3}{4}$ The required line is perpendicular to the given line, therefore its slope is $\frac{-4}{3}$ ⇒ Equation of required line is $\text{y}-\text{y}_1=\text{m}'(\text{x}-\text{x}_1)$ $\text{y}-\frac{4}{3}=\frac{-4}{3}(\text{x}-0)$ $4\text{x}+3\text{y}-4=0$

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