A graph is shown below: dotted line joining ordered pair negative 1, negative 2 and 5, 0 and the region above this line is shaded Which of the following inequalities is best represented by this graph? x − 3y > 5 x − 3y < 5 x − 2y > 5 x − 2y < 5

alrighty
might be helpful to draw or visualize that graph

first find equation of the line that is dotted
we are given points (-1,-2) and (5,0)
the slope between them is hmm
slope between (x1,y1) and (x2,y2) is (y1-y2)/(x1-x2)
for (-1,-2) and (5,0), the slope is (-2-0)/(-1-5)=-2/-6=2/6=1/3

slope intercept form
y=mx+b
m=slope
so slope of 1/3
y=1/3x+b
we gots the opint (5,0)
x=5 and y=0
0=1/3(5)+b
0=5/3+b
b=-5/3

y=1/3x-5/3
now get into standard form
minus y both sides and add 5/3 and times 3
5=x-3y
x-3y=5
alrighty, either of the first 2 equations

ok, so pick a point in the reigon above 5=x-3y
let's pick (0,0)
it should make it true because it is the shaded area

so
x-3y>5?
0-3(0)>5
0>5
nope

so has to be the other one
0-3(0)<5?
0<5
true

so it is x-3y<5

calculista calculista · Answer 2 · 2018-12-16T15:09:19+01:00

Answer:

[tex]x-3y<5[/tex]

Step-by-step explanation:

Step 1

Find the slope of the line

we have

[tex]A(-1,-2),B(5,0)[/tex]

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{0+2}{5+1}[/tex]

[tex]m=\frac{2}{6}[/tex]

[tex]m=\frac{1}{3}[/tex]

Step 2

Find the equation of the line

The equation of the line in the form slope-intercept is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-coordinate of the y-intercept

we have

[tex]m=\frac{1}{3}[/tex]

[tex]B(5,0)[/tex]

substitute

[tex]0=\frac{1}{3}(5)+b[/tex]

[tex]b=-\frac{5}{3}[/tex]

[tex]y=\frac{1}{3}x-\frac{5}{3}[/tex]

[tex]3y=x-5\\x-3y=5[/tex]

The solution is the shaded area above the dotted line

so

the inequality is

[tex]x-3y<5[/tex]

see the attached figure to better understand the problem