Question

If the slope of the line joining points $(k,-3)$ and $(4,5)$ is $\frac{1}{2}$, then the value of $k$ is

• A. $-12$
• B. $12$
• C. $4$
• D. $-4$

Answer 1

The correct option is A $-12$

Let us obtain the equation of the line in slope-intercept form.

The given pair of points is $A(x_1,y_1)=(k,-3),B(x_2,y_2)=(4,5)$

Therefore, the equation of the line $AB$ is

$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

$\Rightarrow \frac{y+3}{5+3}=\frac{x-k}{4-k}$

$\Rightarrow y(4-k)=8x-(5k+12)$

$\Rightarrow y=\frac{8}{4-k}-\frac{5k+12}{4-k}$

Therefore, $\frac{8}{4-k}=\frac{1}{2}$ ......(given)

$\Rightarrow k=-12$