Question

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

Answer 1

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

Answer 2

Answer:

$x-3y$  

Step-by-step explanation:

Step 1

Find the slope of the line

we have

$A(-1,-2),B(5,0)$

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

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{0+2}{5+1}$

$m=\frac{2}{6}$

$m=\frac{1}{3}$

Step 2

Find the equation of the line

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

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

we have

$m=\frac{1}{3}$

$B(5,0)$

substitute

$0=\frac{1}{3}(5)+b$  

$b=-\frac{5}{3}$

$y=\frac{1}{3}x-\frac{5}{3}$  

$3y=x-5\\x-3y=5$

The solution is the shaded area  above the dotted line

so

the inequality is

$x-3y$  

see the attached figure to better understand the problem