give the geometrical representation of 2x+7=0as a equation 1)one variable 2)two variable
Answers
Answer:
Step-by-step explanation:
In one variable,
2y+7=0
⇒2y=−7 ………….(i)
Equation (i) is an equation of one variable i.e., 'y'.
(b) In two variables,
2y+7=0
⇒2y=−7
⇒0x+2y=−7 ……….(ii)
Equation (ii) is represented as an equation of two variables i.e., 'x' and 'y'.
We are given the equation of line as 2y+7=0
(i) Geometric representation of the line 2y+7=0
in one variable.
Since the equation 2y+7=0
is already in one variable i.e. y.
Therefore, we find the value of y to plot the line on the graph.
Shift the value of constant to one side of the equation.
⇒2y=−7
Divide both sides by 2
⇒2y2=−72
Cancel the same terms from numerator and denominator.
⇒y=−72
Write the value in decimal form, y=−3.5
Therefore, we plot the point y=−3.5
on the line.
(ii) Geometric representation of the line 2y+7=0
in two variables
We write the given equation in form of general equation in two variables ax+by+c=0
Therefore 2y+7=0
can be written as 0x+2y+7=0
.
Now we substitute the values of x to get values of y.
When x=0
⇒0×0+2y+7=0
Shift all constants to one side of the equation.
⇒2y=−7
Divide both sides by 2
⇒2y2=−72
Cancel the same terms from numerator and denominator.
⇒y=−72
Write the value in decimal form, y=−3.5
Therefore, the point on the line becomes (0,−3.5)
When x=1
⇒0×1+2y+7=0
Shift all constants to one side of the equation.
⇒2y=−7
Divide both sides by 2
⇒2y2=−72
Cancel the same terms from numerator and denominator.
⇒y=−72
Write the value in decimal form, y=−3.5
Therefore, the point on the line becomes (1,−3.5)
Now we plot the points on the graph and join the points to form a straight line.
Note: Students might get confused in the second part where we have to give geometric representation in two variables as the given equation is in one variable i.e. y. Always write the second variable having the coefficient as 0. Also, while plotting the points on the graph it is always easier if you write the number in decimal form.