Question

Determine the type of boundary line and shading for the graph of the inequality -4x - y < -6

Answer 1

find the intercepts of the line

-4x - y = -6

x-intercept let y = 0 .. so you have -4x = -6

solve for x

now the y intercept, let x = 0

-y = -6

solve for y.


the inequality in the question is < so you can't include any point on the line, so the line is dotted.

Lastly to check which side of the line to shade pick a point like (1, 1)

substitute it and see if its true...

-4(1) - 1 < -6 is -5 < -6 true or false

if true shade the side of the line containing (1,1)

if false shade the opposite side of the line.

hope this helps

Answer 2

um well

Answer 3

Dashed line with shading on the side that includes the origin.

Solid line with shading on the side that does not include the origin.

Dashed line with shading on the side that does not include the origin.

Solid line with shading on the side that includes the origin.

Answer 4

those were the options

Answer 5

well start with a dashed line... thats a fact...

dashed line for < or >

solid line for <= or =>

so subtitute (1, 1) and test

\[-4 \times 1 - 1 < -6\]

is that true or false...?

Answer 6

true?

Answer 7

?

Answer 8

so -5 is less than -6 its false... so (1, 1) isn't in the region

so the graph looks like



you just need to decide to shade above or below the line