solve each box using the answer choices on the side in the picture !

DHGB

Step-by-step explanation:

Let's start with 1.  

The equation is in standard form (ax+by=c): -4x+2y=8

we'll put it into slope intercept form.

Add 4x onto both sides

2y=4x+8

divide by 2

y=2x+4

Parallel lines have the same slope, but a different y intercept. (the line parallel to this one will have a slope of 2 but a y intercept different from +4)

Looking at the answer choices, the only choice with a slope of 2 is D (y=2x-5)

So the answer to 1  is D

Now 2.

we're given 3 points. One of the points crosses the y axis, which is the y intercept. In this case, the line crosses the point (0,3)

That means the y intercept of the line is (0,3)

here's the line so far:

y=mx+3 (m is a placeholder for the slope)

when given a graph, we can use rise/run. Starting from the point (3,2), we can move 3 spaces to the left, and one up.

In a graph, if you move to the left or downwards, it's a negative move. If you move up or to the right, it's a positive move.

Since we went 1 space up (rise) and 3 spaces to the left, (run) the slope is -1/3

So the line is y=-1/3x+3

Perpendicular lines are negative and reciprocal. If you multiply their slopes, they will equal -1. Their y intercepts don't matter at all.

So to find the slope, we can use this equation.

-1/3m=-1

multiply by -3 on both sides

m=3

Looking at the answer choices, H is the only answer with a slope of 3. So the answer to 2 is H.

Now, 3

You can do the graph method like above for 2, but I'll just calculate the slope.

We're given two points, (-1,-2) and (0,2)

the formula for slope is (y2-y1)/(x2-x1)

we can label the points.

x1=-1

y1=-2

x2=0

y2=2

now, substitute into the equation.

m=(2--2)/(0--1)

m=4/1

the slope is 4.

Now let's use point slope form, which is y-y1=m(x-x1)

once again, sub. into the equation.

y+2=4(x+1)

do distributive prop

y+2=4x+4

subtract by 2

y=4x+2

As said above, parallel lines have the same slope.

Looking at the answer options, G also has the slope of 4

so the answer to 3 is G

Finally, #4

Equation: 3x+y=1

subtract 3x from both sides

y=-3x+1

As said above, perpendicular lines have slopes that multiply to equal -1.

-3m=-1

multiply by -1/3

m=1/3

so the slope of the line will be 1/3.

Looking at the answer options, B also has a slope of 1/3.

So the answer to 4 is B

The code is DHGB

Hope this helps!

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

the olimpics is not going to wokk out

step-by-step explanation: