
How do you graph ?
Answer
479.7k+ views
Hint: To plot a graph of any line, we need the points on the Cartesian coordinate plane. The points can be obtained by assuming different values for anyone coordinate and calculating the value for the other coordinate from the equation of a line.
Complete step-by-step answer:
Before plotting the line, first, we get some basic knowledge about the line with the Slope-Intercept equation of the line
Comparing the slope-intercept equation with the given line, we get
and .
The intercept on the Y axes is not , which shows that the line does not pass through the origin.
The slope of the line is greater than , which means the line is tilted more towards the Y-axes.
To plot the line, we start by plotting the X-intercept and Y-intercept
For the X-intercept, we consider y coordinate
Substituting this in the equation of the line
Making the subject of the equation
Hence the X-intercept of the line is .
Now, for the Y-intercept, we consider x coordinate
Substituting this in the equation of the line
Hence the Y-intercept of the line is .
We have two points of the line as and .
Now, we can find some other points on the line.
Let’s suppose some values for the X coordinate and find the corresponding values of the Y coordinate from the equation.
Let’s assume and put this value in the equation of the line
Hence, we get the point with coordinates
Now, let’s assume and put this value in the equation of the line
Hence, we get the point with coordinates
Plotting the four points we obtained , , , and we can plot the line on the graph as shown below.
Note:
To plot a line, only two points are required. But we plot extra points to get a precise line and also to check if any mistake occurred while calculating or plotting the points that don’t fall on the line. Here we assumed the value of the X coordinate and calculated the value of the Y coordinate. The points can also be found by assuming the Y coordinate and calculating the X coordinate respectively.
Complete step-by-step answer:
Before plotting the line, first, we get some basic knowledge about the line with the Slope-Intercept equation of the line
Comparing the slope-intercept equation with the given line, we get
The intercept on the Y axes is not
The slope of the line is greater than
To plot the line, we start by plotting the X-intercept and Y-intercept
For the X-intercept, we consider y coordinate
Substituting this in the equation of the line
Making
Hence the X-intercept of the line is
Now, for the Y-intercept, we consider x coordinate
Substituting this in the equation of the line
Hence the Y-intercept of the line is
We have two points of the line as
Now, we can find some other points on the line.
Let’s suppose some values for the X coordinate and find the corresponding values of the Y coordinate from the equation.
Let’s assume
Hence, we get the point with coordinates
Now, let’s assume
Hence, we get the point with coordinates
Plotting the four points we obtained

Note:
To plot a line, only two points are required. But we plot extra points to get a precise line and also to check if any mistake occurred while calculating or plotting the points that don’t fall on the line. Here we assumed the value of the X coordinate and calculated the value of the Y coordinate. The points can also be found by assuming the Y coordinate and calculating the X coordinate respectively.
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