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**Hint**: In order to determine the slope and intercept to the above equation first rewrite the equation in slope- intercept form as $ y = \dfrac{3}{7}x + \left( { - \dfrac{1}{7}} \right) $ and compare with the general slope-intercept form $ y = mx + c $ , where $ m $ is the slope and $ c $ is the y-intercept and then graph the equation.

**:**

__Complete step-by-step answer__We are given a linear equation in two variables $ x\,and\,y $ i.e, $ - 3x + 7y = - 1 $

Converting the equation into slope intercept form:

For that adding both the sides by $ 3x $ :

$ - 3x + 3x + 7y = - 1 + 3x $

Then dividing by $ 7 $ , which would give $ y $ as a separate term, and we get:

$ \dfrac{{7y}}{7} = \dfrac{{ - 1 + 3x}}{7} $

Separating the denominators on the right side which would give a slope and an intercept of $ y $ -axis.

$ y = \dfrac{3}{7}x + \left( { - \dfrac{1}{7}} \right) $

We obtained an equation in slope-intercept form.

Comparing the above equation with the general slope-intercept form $ y = mx + c $ , where $ m = $ slope and $ c = $ intercept on $ y $ -axis and we get:

$

m = \dfrac{3}{7} \\

c = - \dfrac{1}{7} \;

$

Now for the graph of the equation, we are jumping on the cartesian plane.

There is one most important property of a plane: that the graph to the equation of the form $ ax + by + c = 0 $ is always a straight line.

Graph of equation having y-intercept as $ (0, - \dfrac{1}{7}) $ with slope $ m = \dfrac{3}{7} $

Hence, we’ve successfully plotted our graph of $ y = \dfrac{3}{7}x + \left( { - \dfrac{1}{7}} \right) $

Therefore, the slope and intercept to expression is $ - 3x + 7y = - 1 $ equal to $ \dfrac{3}{7}and\, - \dfrac{1}{7} $ respectively.

**Note**: 1. Cartesian Plane: A Cartesian Plane is given its name by the French mathematician Rene Descartes, who first used this plane in the field of mathematics. It is defined as the two mutually perpendicular number lines, the one which is horizontal is given the name x-axis and the one which is vertical is known as the y-axis. With the help of these axes we can plot any point on this cartesian plane with the help of an ordered pair of numbers.

2.Slope-Intercept Form= $ y = mx + c $

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