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

Mar 4, 2018

$3$

Explanation:

Suppose,the equation of the line is $y = m x + c$,where, $m$ is the slope and $c$ is the intercept.

So, putting the given values of coordinates through which it passes we get,

$3 = m + c$...1

and, $6 = 2 m + c$...2

solving, 1 & 2 we get,

$m = 3$

Mar 4, 2018

$\setminus q \quad \setminus q \quad \text{slope of line between" \ ( 1, 3 ) \quad "and} \setminus \quad \left(2 , 6\right) \setminus = \setminus 3 \setminus .$

Explanation:

$\text{Recall the definition of the slope of a line between two points: }$

$\setminus \quad \text{slope of line between" \ ( x_1, y_1 ) \quad "and} \setminus \quad \left({x}_{2} , {y}_{2}\right) \setminus = \setminus \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} .$

$\text{Applying this definition to our two given points, we get:}$

$\setminus \quad \text{slope of line between" \ ( 1, 3 ) \quad "and} \setminus \quad \left(2 , 6\right) \setminus = \setminus \frac{\left(6\right) - \left(3\right)}{\left(2\right) - \left(1\right)}$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad = \setminus \frac{3}{1} \setminus = \setminus 3.$

$\text{So, we conclude:}$

$\setminus q \quad \setminus q \quad \text{slope of line between" \ ( 1, 3 ) \quad "and} \setminus \quad \left(2 , 6\right) \setminus = \setminus 3 \setminus .$