I’ve been at this for 3 hours. Please help.

1. y=1/2x-3

First thing to remember is the formula:

y=mx+b

m represents the slope

and b represents the y-intercept

so for the first problem m would be 1/2, which means the slope would be 1/2

y intercept for this problem would be -3

graphing first equation:

since our y intercept is -3 we would go down 3 points, so put a dot at (0,-3)

plug in 0 for y and solve

0=1/2x-3

+3 +3

3=1/2x-0

3=1/2x

multiply each side by 2

6=2 * 1/2x (we do this to get rid of the 1/2)

6=1x

divide by 1

6=x

then you can put another dot at (6,0) then draw the line

2. 3x+y=2

this equation is different because it isnt in y=mx+b form, so you have to do some algebra

3x+y=2

subtract 3x from both sides to get:

y=-3x+2

now looking back that m represents slope and b represents y intercept

slope in this case would be -3 and y intercept would be 2

graphing second equation:

since the y intercept for this problem is 2 we would go up 2 so put a dot at (0,2)

set the equation to 0 (when y is zero x is...) again find the other coordinate value:

0=-3x+2

-2 -2

-2=-3x

divide by -3

2/3=x

(two negatives make a positive)

the best way to put the dot is put it close to the half mark between one and zero

then draw the line

3. this problem is the same as the previous one but you do exactly the same thing as before

2x-y=3

-2x -2x

-y=3-2x

multiply by -1 to get rid of the negative (2 becomes positive in this case but the 3 becomes negative)

y=2x-3

slope for this problem would be 2 and the y intercept would be -3

graphing third equation:

since the y intercept is -3 we would go down 3 points, so put a dot at (0,-3)

again solve for 0 for this equation

0=2x-3

+3 +3

3=2x

divide by two on both sides

3/2=x

3/2 is same as 1.5

put the dot between 1 and 2 directly in the middle (1.5,0)

then draw the line

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

you are playing an adventure game on your computer. you come across a troll who won't let you pass and there is no other way to get to the other side of the river except over the bridge he is guarding.

the troll is a nerd. he takes great delight in watching people struggle with his problems. very few get them. he only gives you one chance and then he changes the puzzle. you have to solve this one.

before you are four blocks. they are numbered 11,6, -7,21.

he tells that the answer he wants is minus and between -1 and - 2. you can use +, -, ×, ÷   ( and ) as many times as you like or no times at all. you don't like the way he's looking at you, but you need to cross the bridge. what do you do?