Question

Please tell the answer and show the work.

Answer 1

First step, i would try to figure out the slope. think of it as a typical y=mx+b linear equation as you check out the graph.

it's just rise over run (rise up this many, run over that many), and your options are (-2/3) or (-3/2)

start at the y-intercept, which is just above the middle of the graph. if you go down 2 and try to go over 3, you hit the line before you can count 3 units. that means this slope is incorrect.

go back to the y-intercept. down 3, over 2--there you go. your slope here is (-3/2), which immediately gets rid of half your answer choices for having the wrong slope

the next thing you have to do is decide where this graph should be shaded. the shaded region shows the domain; the white region shows what's outside of your domain. this inequality is shaded "below" which means that the y values are LESS than "(-3/2)x +1"

that eliminates another one of your answer choices; choice 3 is correct. the inequality is y < (-3/2)x + 1

if the graphs of inequalities are shaded below and the line is dotted, it's less than. if the graphs of inequalities are shaded above and the line is dotted, it's greater than. general rules for ya

Answer 2

The third one is the answer but unless you plot it there is not much work you can show