Find parametric equations for the line that passes through the point (5, 2) and is parallel to the line y=−72x−2

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Find parametric equations for the line that passes through the point (5, 2) and is parallel to the line  y=−72x−2

Marian Tucker · Accepted Answer

Step 1The given line equationy=−72x−2comaparing with the&amp;nbsp;y=mx+b, we getm=−72&amp;nbsp;and&amp;nbsp;b=−2The slope of the line is&amp;nbsp;−72Considering that the line traverses the point&amp;nbsp;(5,&amp;nbsp;2)&amp;nbsp;is parallel to the line&amp;nbsp;y=−72x−2We are aware that a parallel line has a constant slope.So, the line passes trough the point&amp;nbsp;(5,&amp;nbsp;2)&amp;nbsp;has slope&amp;nbsp;m=−72Step 2usin⁡g&amp;nbsp;point slope formula,y−y1=m(x−x1)Here&amp;nbsp;m=−72,&amp;nbsp;(x1,&amp;nbsp;y1)=(5,&amp;nbsp;2)⇒y−2=−72(x−5)⇒y−2−7=x−52=t(≤t)Now,&amp;nbsp;y−2−7=t&amp;nbsp;⇒y−2=−7t&amp;nbsp;⇒y=2−7tand&amp;nbsp;x−52=t⇒x=2t&amp;nbsp;⇒x=5+2tso, parametric equations for the line that passes through the point&amp;nbsp;(5,&amp;nbsp;2)&amp;nbsp;isy=2−7t,&amp;nbsp;x=5+2tThis is the required answer.

Find parametric equations for the line that passes through the

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