# Question #313d2

Feb 10, 2017

See below

#### Explanation:

There are two standard forms and the format you presented is that of: $y = m x + c$

$y$ is the dependant variable. Its value is 'dependant' on what value you assign to $x$

$x$ is the independent variable to which you may assign any value you so chose, unless restricted by the conditions of the question.

$m$ is the gradient (slope) which is always read from left to right on the x-axis. It is : $\left(\text{change in up or down")/("change in along}\right)$

$c$ is the constant and in this equation type and it is where the plotted line crosses the y-axis.

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The other standard form uses just $m$ in relation to 2 fixed points. The value of $c$ is directly related to these points, thus can be determined by algebraic manipulation.

Let point 1 be ${P}_{1} \to \left({x}_{1} , {y}_{1}\right)$
Let point 2 be ${P}_{2} \to \left({x}_{2} , {y}_{2}\right)$

Then the equation takes the form:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$