Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you write $2 x - 3 y > 7$ $2x - 3y > 7$ in slope intercept form?

1 Answer

Aug 7, 2015

The boundary can be written in slope-intercept form giving
$XXXX$ $color(white)("XXXX")$ $y < \frac{2}{3} x + (- \frac{7}{3})$ $y < 2/3x+(-7/3)$

Explanation:

given $2 x - 3 y > 7$ $2x-3y > 7$

adding $3 y$ $3y$ to both sides
$XXXX$ $color(white)("XXXX")$ $2 x > 3 y + 7$ $2x > 3y+7$

subtracting 7 from both sides
$XXXX$ $color(white)("XXXX")$ $2 x - 7 > 3 y$ $2x-7 > 3y$

dividing both sides by $3$ $3$
$XXXX$ $color(white)("XXXX")$ $\frac{2}{3} x - \frac{7}{3} > y$ $2/3x-7/3 > y$

Reversing the sides
$XXXX$ $color(white)("XXXX")$ $y < \frac{2}{3} - \frac{7}{3}$ $y < 2/3-7/3$

or (in explicit slope-intercept form
$XXXX$ $color(white)("XXXX")$ $y < (\frac{2}{3}) x + (- \frac{7}{3})$ $y < (2/3)x + (-7/3)$
where the boundary line has a slope of $\frac{2}{3}$ $2/3$ and a y-intercept of $(- \frac{7}{3})$ $(-7/3)$

Related questions

See all questions in Linear Inequalities in Two Variables

Impact of this question

2623 views around the world

You can reuse this answer
Creative Commons License