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Question: How do you graph using slope and intercept of \( - 3x + 7y = - 1 \) ?...

How do you graph using slope and intercept of −3x+7y=−1- 3x + 7y = - 1 ?

Explanation

Solution

Hint : In order to determine the slope and intercept to the above equation first rewrite the equation in slope- intercept form as y=37x+(−17)y = \dfrac{3}{7}x + \left( { - \dfrac{1}{7}} \right) and compare with the general slope-intercept form y=mx+cy = mx + c , where mm is the slope and cc 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 yx\,and\,y i.e, −3x+7y=−1- 3x + 7y = - 1
Converting the equation into slope intercept form:
For that adding both the sides by 3x3x :
−3x+3x+7y=−1+3x- 3x + 3x + 7y = - 1 + 3x
Then dividing by 77 , which would give yy as a separate term, and we get:
7y7=−1+3x7\dfrac{{7y}}{7} = \dfrac{{ - 1 + 3x}}{7}
Separating the denominators on the right side which would give a slope and an intercept of yy -axis.
y=37x+(−17)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+cy = mx + c , where m=m = slope and c=c = intercept on yy -axis and we get:
m=37 c=−17   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=0ax + by + c = 0 is always a straight line.
Graph of equation having y-intercept as (0,−17)(0, - \dfrac{1}{7}) with slope m=37m = \dfrac{3}{7}
Hence, we’ve successfully plotted our graph of y=37x+(−17)y = \dfrac{3}{7}x + \left( { - \dfrac{1}{7}} \right)
Therefore, the slope and intercept to expression is −3x+7y=−1- 3x + 7y = - 1 equal to 37and −17\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+cy = mx + c