Question

Express y in terms of x, it is given that 3x -2y = 6. Check whether (1,2) is on the line represented by the equation 3x -2y = 6. Draw its graph and also, find the value of y at x = 4.
A. y =3
B. y = 6
C. y = 1
D. y = 4

Answer 1

Hint: First we will write y in terms of x and then put x = 1 to check whether we get y = 2. After this we will draw the graph of the 3x -2y = 6 on the graph paper. And lastly we will find the value of y at x = 4.

Complete step-by-step answer:
The given equation is:
3x -2y = 6 ---- (1)
Putting the value of x =1 and y = 2, we get:
LHS = $3 \times 1 - 2 \times 2 = 3 - 4 = - 1$ $ \ne $ RHS
So this point doesn’t lie on the line.
y can be expressed in terms of x as follow:
$ \Rightarrow {\text{y = }}\dfrac{{3{\text{x - 6}}}}{2}$
At x = 0,
y = $\dfrac{{3 \times 0 - 6}}{2} = - 3$
At y = 0,
x= $\dfrac{6}{3} = 2$.
The graph of the above equation is as follow:

From the graph, we can say that the value of y at x = 4 is 3 denoted by C(4,3).

Note: In the question involving drawing graphs of a two variable linear equation, you should express the dependent variable in terms of independent variable and then get two points in the XY plane to draw the graph. The slope of the line of the form ax+by = c is given as m= $\dfrac{{ - a}}{b}$.