Question

How do you graph $ y=-\dfrac{2}{3}x+4 $ .

Answer 1

Hint:
 The above-given question is of the graph of a linear equation. To draw the line given above we will at first find a minimum three-point which lie on the line and then we will plot all those points on the graph and then join these points with the help of the ruler. The line which we have obtained will be the graph of $ y=-\dfrac{2}{3}x+4 $.

Complete step by step answer:
We know that the above question is of a linear equation.
Since we have to draw the graph of the equation $ y=-\dfrac{2}{3}x+4 $ so will at first find a minimum three-point which lies on the given line equation.
Since, we know that $ y=-\dfrac{2}{3}x+4 $ , so when x = 0, we will get:
 $ \begin{align}
  & \Rightarrow y=-\dfrac{2}{3}\times 0+4 \\
 & \Rightarrow y=4 \\
\end{align} $
Now, when y = 0, we will get:
 $ \begin{align}
  & \Rightarrow 0=-\dfrac{2}{3}x+4 \\
 & \Rightarrow x=\dfrac{4\times 3}{2} \\
 & \Rightarrow x=6 \\
\end{align} $
Now, when x = 3,we will get:
 $ \begin{align}
  & \Rightarrow y=-\dfrac{2}{3}\times 3+4 \\
 & \Rightarrow y=2 \\
\end{align} $
So, we will arrange the above value y corresponding to different value of x in the below table:

x	6	0	3
y	0	4	2

Now, we will plot all the above point on the graph, we will get:

Now, to get the graph of $ y=-\dfrac{2}{3}x+4 $ we will join all the plotted points with the help of a ruler.
Thus, the line which we obtain after joining all the points is our required graph.

This is our required solution.

Note:
Student are required to note that in $ y=-\dfrac{2}{3}x+4 $, we have a coefficient of y is 1, so the coefficient of x is equal to the slope of the given line because the general equation of the slope-intercept form of the line is given as y = mx + c, where m is the slope of the line and c is the y-intercept of the line.