Question

What is the slope of the line passing through the following points $\left( {5,2} \right),\left( {11,11} \right)$?

Answer 1

The slope of a line is a number that measures its steepness, usually denoted by the letter $m$.
Also we know that:
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
So by using the above equation we can find the slope of the line passing through the given points.

Complete step by step solution:
Given
$\left( {5,2} \right),\left( {11,11} \right)............................................\left( i \right)$
Now we have to find the slope of the line passing through the given points.
So for finding the slope of a line we have the equation:
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}..................................\left( {ii} \right)$
Such that we have to find the corresponding values and substitute it in the equation (ii) to find the slope.
So on comparing with (i) we can write:
${x_1} = 5 \\\ {x_2} = 11 \\\ {y_1} = 2 \\\ {y_2} = 11 \\\$
Substituting the above values in (ii) we can write:
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} \\\ = \dfrac{{11 - 2}}{{11 - 5}} \\\ = \dfrac{9}{6} \\\ = \dfrac{{3 \times 3}}{{3 \times 2}} \\\ = \dfrac{3}{2} \\\ = 1.5..........................\left( {iii} \right) \\\$
Therefore from (iii) we can write that the slope of the line passing through the given points$\left( {5,2} \right),\left( {11,11} \right)$ would be $1.5$.

Note: The slope of a line can be positive, negative, zero or undefined.
Positive slope: Here, y increases as x increases, so the line slopes upwards to the right. The slope will be a positive number.
Negative slope: Here, y decreases as x increases, so the line slopes downwards to the right. The slope will be a negative number.
Zero slope: Here, y does not change as x increases, so the line is exactly horizontal. The slope of any horizontal line is always zero.
Undefined slope: When the line is exactly vertical, it does not have a defined slope. The two x coordinates are the same, so the difference is zero.