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How do you graph the line that passes through the origin parallel to the line x+y=10?

Answer
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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 y=mx, where m = slope. The value of m will be equal to the value of the slope of the given line x+y=10. Now, to find the slope of x+y=10 we will compare it with the general form y=mx+c, 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 x+y=10.
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 y=mx+c, 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,
y=mx
Now, since the above line is parallel to the line x+y=10, as stated in the question, so their slopes will be equal. We can write the equation of line x+y=10 in slope intercept form as:
y=x+10
On comparing it with the general form y=mx+c we get m=1, so the equation of the assumed line becomes:
y=xx+y=0...............(i)
Therefore, the plot of the two lines x+y=0 and x+y=10 can be shown as below:
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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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