How do you write an equation (a) in slope intercept form and (b) in standard form for the line passing through (1,8) and perpendicular to 2x+5y=1?

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Answer 1 · 2016-12-15T18:50:07

Please see the explanation.

To make any line that is perpendicular to a line in standard form:

#ax + by = c#

Swap "a" and "b" and, if "b" was negative then make it positive, otherwise, change the sign of "a". Therefore, a line that is perpendicular to:

#2x + 5y = 1#

Will have the form:

#5x - 2y = c#

To make it pass through the point #(1,8)#, substitute the point into the above and then solve for c:

#5(1) - 2(8) = c#

#c = -11#

The standard form is

#5x - 2y = -11#

The slope intercept form is

#y = 5/2x + 11/2#