Question

Find a point that lies on the line, which passes through the point $(2,5)$ shown in the figure and whose slope is $-\frac{2}{3}$ .

• A. $A(-1,3)$
• B. $B(0,8)$
• C. $C(4,2)$
• D. $D(5,3)$
• E. $E(5,7)$

Answer 1

The correct option is D $D(5,3)$

Since $\frac{-2}{3}$ is the slope of the line and $(2,5)$ is a point lying on the line, then the equation of the line is given by
$\frac{y-5}{x-2}=\frac{-2}{3}$

$\Rightarrow 3y-15=-2x+4$

$\Rightarrow 2x+3y=19$.
Hence, any point lying on the line will be of the form $(x,\frac{19-2x}{3})$.

Hence for $x=5$, we get the point as $(5,\frac{19-10}{3})=(5,3)$