Question 1131822
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The slope of the given line is 5/2; the slope of a line perpendicular to the given line is -2/5.<br>
So the equation in slope-intercept form of the line perpendicular to the given line is<br>
{{{y = (-2/5)x+b}}}<br>
The value of b can be found using the given point (5,1) on the line:<br>
{{{1 = (-2/5)5+b}}}
{{{1 = -2+b}}}
{{{b = 3}}}<br>
In slope-intercept form, the equation of the line is<br>
{{{y = (-2/5)x+3}}}<br>
Convert to the required form:<br>
{{{5y = -2x+15}}}
{{{2x+5y = 15}}}