Question

What is the slope of the line that passes through the points $(1,3)$ and $(2,6)?$

Answer 1

We know that slope of the lone is also known as the gradient of a line that gives the direction and steepness of the line. If we have two coordinates $({x_1},{y_1})$ and $({x_2},{y_2})$, then the slope of the line passing through these points is as follows: slope $= \dfrac{{({y_2} - {y_1})}}{{({x_2} - {x_1})}}$ . Applying this formula we will compare the values and solve them.

Complete step by step solution:
We have been given the points $(1,3)$ and $(2,6)$ through which the line passes. Now we take the slope of a line passing through the points and the formula is $\dfrac{{({y_2} - {y_1})}}{{({x_2} - {x_1})}}$ .
So we have ${x_1} = 1,{y_1} = 3,$ ${x_2} = 2$ and ${y_2} = 6$.
By applying this to the definition of two given points we get: $\dfrac{{6 - 3}}{{2 - 1}} = \dfrac{3}{1}$.
Hence we get the slope of the line passing through the points $(1,3)$ and $(2,6)$ is $3$.

Note:
We should note that if the slope of the line is zero then it is parallel to $x -$axis and if the slope tends to infinity then it is perpendicular to the $x -$ axis i.e. it makes an angle of ${90^ \circ }$ with the $x -$axis. We should remember that if the x- coordinate of the two points through which line passes are same then it must be perpendicular to the x- axis.