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Mathematics

Find x, if the slope of the line joining (x, 2) and (8, -11) is −34-\dfrac{3}{4}.

Straight Line Eq

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Answer

By formula,

Slope = y2−y1x2−x1\dfrac{y2 - y1}{x2 - x1}

Given, slope of line joining (x, 2) and (8, -11) is −34-\dfrac{3}{4}.

∴−34=−11−28−x⇒−3(8−x)=4×−13⇒−24+3x=−52⇒3x=−52+24⇒3x=−28⇒x=−283.\therefore -\dfrac{3}{4} = \dfrac{-11 - 2}{8 - x} \\[1em] \Rightarrow -3(8 - x) = 4 \times -13 \\[1em] \Rightarrow -24 + 3x = -52 \\[1em] \Rightarrow 3x = -52 + 24 \\[1em] \Rightarrow 3x = -28 \\[1em] \Rightarrow x = -\dfrac{28}{3}.

Hence, x = −283-\dfrac{28}{3}.

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