Question 1066241
Find the equation of straight line which is parallel to 2x+3y=11 and such that the sum of intercepts on axes is 15.
:
Find the slope of the given equation, put in the slope/intercept form:
2x + 3y = 11
3y = -2x + 11
y = {{{-2/3}}}x + {{{11/3}}}
parallel lines have the same slope, find the parallel line
Given that intercepts: x + y = 15, therefore
y = (15-x)
the y intercept occurs when x = 0; therefore we can say
y = {{{-2/3)))x + (15-x)
the x intercept occurs when y = 0; therefore
{{{-2/3}}}x + (15-x) = 0
{{{-2/3}}}x = -(15-x)
multiply both sides by -1
{{{2/3}}}x = 15 - x
add x to both sides
{{{5/3}}}x = 15
x = 15 *{{{3/5}}}
x = 9 is the x intercept
and
15-9 = 6 is the y intercept
:
See what that looks like
{{{ graph( 300, 200, -6, 15, -10, 15, (-2/3)x+(11/3), (-2/3)x+6) }}}
Green line is our parallel line; intercepts x=9; y=6