How do you graph \[y=2x-9\]?
Answer
Verified
448.2k+ views
Hint: Suppose an equation of straight line to be \[y=ax+b\]. We can draw the graph of \[y=ax+b\] from the simple graph \[y=x\]. We need to modify the \[y=x\] graph by shifting and scaling methods. It is a better idea to modify the graph of \[y=x\] in such a manner that we get the required graph by going from left side to right side of the equation \[y=2x-9\].
As per the given question, we need to graph a straight line which is given by the equation \[y=2x-9\].
A straight line can be traced out on the cartesian plane by just two points lying on it. We can also use a third point for sort of check. It is very simple to graph the \[y=x\] line as it is symmetric to both x and y axes.
The graph of \[y=x\] is as shown in below figure:
If we go from left hand side to right hand side of the equation \[y=2x-9\], it is clear that we need to first scale the \[y=x\] graph by a factor 2. Then we get, \[y=2x\].
And the graph of \[y=2x\] is as shown in the below figure:
Now, we need to shift the \[y=2x\] graph right hand side by \[\dfrac{9}{2}\] units to get the required straight line \[y=2x-9\]. And the graph of \[y=2x-9\] is shown in the below figure:
\[\therefore \] We have to compress \[y=x\] by 2 and then shift it to the right hand side by \[\dfrac{9}{2}\] units to get the desired line \[y=2x-9\].
Note:
We can trace the graph of \[y=2x-9\] by substitution by any two random values of x. We can also trace the graph by going from the right hand side to left hand side of the straight-line equation \[y=2x-9\]. So, by taking 2 common, we get \[y=2(x-\dfrac{9}{2})\]. That is, we have to shift the \[y=x\] graph by \[\dfrac{9}{2}\] units and then compress it by a factor 2 to get the graph of \[y=2x-9\].
As per the given question, we need to graph a straight line which is given by the equation \[y=2x-9\].
A straight line can be traced out on the cartesian plane by just two points lying on it. We can also use a third point for sort of check. It is very simple to graph the \[y=x\] line as it is symmetric to both x and y axes.
The graph of \[y=x\] is as shown in below figure:
If we go from left hand side to right hand side of the equation \[y=2x-9\], it is clear that we need to first scale the \[y=x\] graph by a factor 2. Then we get, \[y=2x\].
And the graph of \[y=2x\] is as shown in the below figure:
Now, we need to shift the \[y=2x\] graph right hand side by \[\dfrac{9}{2}\] units to get the required straight line \[y=2x-9\]. And the graph of \[y=2x-9\] is shown in the below figure:
\[\therefore \] We have to compress \[y=x\] by 2 and then shift it to the right hand side by \[\dfrac{9}{2}\] units to get the desired line \[y=2x-9\].
Note:
We can trace the graph of \[y=2x-9\] by substitution by any two random values of x. We can also trace the graph by going from the right hand side to left hand side of the straight-line equation \[y=2x-9\]. So, by taking 2 common, we get \[y=2(x-\dfrac{9}{2})\]. That is, we have to shift the \[y=x\] graph by \[\dfrac{9}{2}\] units and then compress it by a factor 2 to get the graph of \[y=2x-9\].
Recently Updated Pages
One difference between a Formal Letter and an informal class null english null
Can anyone list 10 advantages and disadvantages of friction
What are the Components of Financial System?
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Trending doubts
10 examples of friction in our daily life
Difference Between Prokaryotic Cells and Eukaryotic Cells
What is the specific heat capacity of ice water and class 11 physics CBSE
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
State and prove Bernoullis theorem class 11 physics CBSE
State the laws of reflection of light