Question

Draw the graph for the linear equation $3y = 2x - 4$ . Which of the following is correct?
(A) The line passes through $(0,2)$ and $m = \dfrac{{ - 2}}{3}$
(B) The line passes through $(0,2)$ and $m = \dfrac{2}{3}$
(C) The line passes through $(2,0)$ and $m = \dfrac{{ - 2}}{3}$
(D) The line passes through $(2,0)$ and $m = \dfrac{2}{3}$

Answer 1

Hint: While converting a linear equation into a graph, we usually consider $y$ as dependent variable and $x$ as independent variable. $x$ is on the horizontal axis and $y$ is on the vertical axis. In order to draw a graph, we require one point and the slope or two points.
A usual way of representing a line is: $y = mx + c$ where m is the slope of the line and c is the y-intercept.

Complete answer:
The linear equation given in the above question is: $3y = 2x - 4$
Now let’s try to convert it into standard form, $y = mx + c$
We have to make the coefficient of $y$ as 1.
Dividing the entire equation by 3, we get: $y = \dfrac{{2x - 4}}{3} = \dfrac{2}{3}x - \dfrac{4}{3}$
Comparing this with the general equation, we know that: $m = \dfrac{2}{3}$
Hence, we can rule out options A and D.
When $x = 0$ , substituting it in the given equation, we get: $3y = - 4$
Therefore, $y = \dfrac{{ - 4}}{3}$
When $y = 0$ , substituting it in the given equation we get: $2x - 4 = 0$
Therefore, $x = 2$
The given line passes through $(0,\dfrac{{ - 4}}{3})$ and $(2,0)$
Let’s draw the graph of the equation:

Therefore, the correct option is B

Note: For drawing a graph of a line, we need either a point and slope or two points. After drawing the line, one can use a graph paper and easily find out the points the line is passing through. A slope is nothing but the tangent of the angle between the line and the x-axis measured in anti-clockwise direction. One should be careful with the general equation and m sign convention.