Question

How do you graph\[2y-6x=10\]?

Answer 1

Hint: To plot the graph for the given equation, first of all we should know the straight line equation and slope- intercept form. First of all convert the given equation into slope-intercept form. Then find out the slope and ordered pair by that equation and then we can plot the graph easily.

Complete step by step answer:
From the given question, we are going to plot a graph for\[2y-6x=10\].
Let us consider
\[2y-6x=10.....\left( 1 \right)\]
By observing equation (1) we can say that equation (1) is an equation of straight line.
So, for plotting the graph for equation (1), we have to convert the equation (1) into slope-intercept form. Then we can easily plot the graph by y-intercept and slope.
Slope- intercept formula is
\[y=mx+b\]
Let us consider
\[y=mx+b......\left( f1 \right)\]
Let us compute equation (1) in the form of formula (f1).
Transferring \[-6x\]from LHS to RHS
\[2y=6x+10\]
Let us consider
\[2y=6x+10......\left( 2 \right)\]
Dividing equation (2) by 2, we get
\[\dfrac{2y}{2}=\dfrac{6x}{2}+\dfrac{10}{2}\]
\[\Rightarrow y=3x+5\]
Let us consider
\[\Rightarrow y=3x+5........\left( 3 \right)\]
Comparing equation (3) with formula (f1), we get
m=3 and b=5.
The slope is 3 and the y-intercept is 5. The y-intercept is the point (0, 5). The slope is\[\dfrac{3}{1}\]. So you can place a point at the y-intercept and move up 3 places and over to the right 1 to get another point. You can also go down 3 places and over to the left 1 place to get another point.
You can also determine ordered pairs using the equation.
\[\begin{align}
  & \text{x y} \\
 & \text{0, 5} \\
 & \text{2, 11} \\
 & \text{4, 17} \\
\end{align}\]
So, by the ordered pairs the graph of the equation (1) is

Note: Students should be well aware of plotting straight line graphs. Questionnaire may ask to draw a circle or any other geometry graphs. So please be aware of all the geometry. Students should also avoid calculation mistakes while solving this problem.