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

`x-3y<5`

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=(y2-y1)/(x2-x1)`

substitute

`m=(0+2)/(5+1)`

`m=(2)/(6)`

`m=(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=(1)/(3)`

`B(5,0)`

substitute

`0=(1)/(3)(5)+b`

`b=-(5)/(3)`

`y=(1)/(3)x-(5)/(3)`

`3y=x-5\\x-3y=5`

The solution is the shaded area above the dotted line

so

the inequality is

`x-3y<5`

see the attached figure to better understand the problem

Answer 2

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