Question

find three points with integer valued coordinates that solve the equation -2x-3y=-7

Answer 1

Answer:

(-1, 3), (2, 1), (5, -1)

Step-by-step explanation:

We have the equation of the line in the standard form:

$Ax+By=C$

Convert to the slope-intercept form:

$y=mx+b$

$-2x-3y=-7$              add 2x to both sides

$-3y=2x-7$           divide both sides by (-3)

$y=-\dfrac{2}{3}x+\dfrac{7}{3}$

for x = -1

$y=-\dfrac{2}{3}(-1)+\dfrac{7}{3}=\dfrac{2}{3}+\dfrac{7}{3}=\dfrac{2+7}{3}=\dfrac{9}{3}=3\to(-1,\ 3)$

for x = 2

$y=-\dfrac{2}{3}(2)+\dfrac{7}{3}=-\dfrac{4}{2}+\dfrac{7}{3}=\dfrac{-4+7}{3}=\dfrac{3}{3}=1\to(2,\ 1)$

for x = 5

$y=-\dfrac{2}{3}(5)+\dfrac{7}{3}=-\dfrac{10}{3}+\dfrac{7}{3}=\dfrac{-10+7}{3}=\dfrac{-3}{3}=-1\to(5,\ -1)$