Find if possible, the slope of the line through the points $(1/2,3/4)$ and $(-1/3,5/4)$

Since slope of line passing through two points $\left( { x }_{ 1 },{ y }_{ 1 } \right)$ and $\left( { x }_{ 2 },{ y }_{ 2 } \right)$ is ${ m }=\dfrac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } }$

We now find the slope of the line passing through the points $\left( \dfrac { 1 }{ 2 } ,\dfrac { 3 }{ 4 } \right)$ and $\left( -\dfrac { 1 }{ 3 } ,\dfrac { 5 }{ 4 } \right)$ as shown below:

${ m }=\dfrac { \frac { 5 }{ 4 } -\frac { 3 }{ 4 } }{ -\frac { 1 }{ 3 } -\frac { 1 }{ 2 } } =\dfrac { \frac { 2 }{ 4 } }{ -\frac { 5 }{ 6 } } =\dfrac { \frac { 1 }{ 2 } }{ -\frac { 5 }{ 6 } } =\dfrac { 1 }{ 2 } \times -\dfrac { 6 }{ 5 } =-\dfrac { 6 }{ 10 } =-\dfrac { 3 }{ 5 }$

Therefore, the slope of the line is

$-\dfrac { 3 }{ 5 }$

.