Question 551321
Start with the general form in slope-intercept form:
{{{y = mx+b}}}
Find the slope of the given line whose equation is:
{{{2x+y = 7}}} rewrite in slope-intercept form:
{{{y = -2x+7}}} The slope, {{{m = -2}}}.
The slopes of perpendicular lines are negative reciprocals.
The slope of the new line is:
{{{-(-1/2) = 1/2}}}, so...
{{{y = (1/2)x+b}}} To find b substitute the x- and y-coordinates of the given point (4, 4) and solve for b.
{{{4 = (1/2)4+b}}}
{{{b = 2}}}, finally:
{{{y = (1/2)x+2}}} is the final equation.