
How do you graph the line that passes through the origin parallel to the line ?
Answer
453.9k+ views
Hint: First we will find the equation of the line. To do this, we will assume the required equation of the line passing through the origin in slope intercept form as , where m = slope. The value of m will be equal to the value of the slope of the given line . Now, to find the slope of we will compare it with the general form , where c = y – intercept. Once the value of slope is found we will easily plot the graph.
Complete step by step solution:
Here, we have been asked to plot the graph of a line which passes through the origin and is parallel to the line .
Now, to plot the graph first we need to determine the equation of the required line. We know that the general equation of the line in slope intercept form is given as , where m = slope and c = y – intercept. It has been given to us that the line is passing through the origin, so the y – intercept will be 0. Therefore, the equation of the line becomes,
Now, since the above line is parallel to the line , as stated in the question, so their slopes will be equal. We can write the equation of line in slope intercept form as:
On comparing it with the general form we get , so the equation of the assumed line becomes:
Therefore, the plot of the two lines and can be shown as below:
Note: It is necessary to determine the equation of the line because it will be difficult to draw the graph if we don’t know the equation of line. Always remember that when a line passes through the origin then its y – intercept is 0. This can be proved by considering the fact that if the line passes through the origin then it will satisfy the point O (0, 0), i.e. the origin.
Complete step by step solution:
Here, we have been asked to plot the graph of a line which passes through the origin and is parallel to the line
Now, to plot the graph first we need to determine the equation of the required line. We know that the general equation of the line in slope intercept form is given as
Now, since the above line is parallel to the line
On comparing it with the general form
Therefore, the plot of the two lines

Note: It is necessary to determine the equation of the line because it will be difficult to draw the graph if we don’t know the equation of line. Always remember that when a line passes through the origin then its y – intercept is 0. This can be proved by considering the fact that if the line passes through the origin then it will satisfy the point O (0, 0), i.e. the origin.
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