Question

PLEASE HELP ILL DO THE SAME PLEASE AND I NEED STEP BY STEP IM TRYING TO LEARN :(

Answer 1

Answer:

5)

Line 1: $y=-x+3$

Line 2: $y=3x-3$

6)

Line 1: $y=\frac{1}{2}x-2$

Line 2: $y=-\frac{5}{2}x+6$

7)

See below

Step-by-step explanation:

To write the system of equations on the graph, you just need to write the 2 equations of the 2 lines.

5)

The first thing to do is find the slope of the lines. Pick one of them, and start by finding 2 points on that line that land perfectly on the grid.

It's pretty hard to read that top graph in the photo, but I think I see these ones marked:

Line 1: (0, 3) and (3, 0)

Line 2: (0, -3) and (2, 3)

Make sure I got them correct, because the equations will be wrong otherwise. Same for problem 6. To find the slope, divide the change in y by the change in x. Starting with line 1, y went from 3 to 0, so a change of -3. x went from 0 to 3, so a change of 3.

Divide the change in y by the change in x:

$m=\frac{y2-y1}{x2-x1}\\\\m=\frac{0-3}{3-0}\\\\m=\frac{-3}{3}\\\\m=-1$

The slope of line 1 is -1. That means every time x increases by 1, y decreases by 1. You can see that on the line.

Now for line 2:

$m=\frac{3--3}{2-0}\\\\m=\frac{6}{2}\\\\m=3$

When x increases by 1, y increases by 3.

The last thing to do is find the y-intercept of both lines. That's just where the line intersects the y-axis, at x = 0, and it's clearly visible on the graph so there isn't much to do.

Line 1: 3

Line 2: -3

Now, you can write the equations for these lines in slope intercept form:

$y=mx+b$

where m is the slope and b is the y-intercept we found above.

Line 1: $y=-x+3$

Line 2: $y=3x-3$

In line 1, -1x can be simplified to just -x.

6)

I'll do the exact same process here, but with less explaining. Let me know if you have any questions.

Find 2 points:

Line 1: (0, -2) and (4, 0)

Line 2: (0, 6) and (4, -4)

Find the slope of line 1:

$m=\frac{y2-y1}{x2-x1}\\\\m=\frac{0--2}{4-0}\\\\m=\frac{1}{2}$

and line 2:

$m=\frac{-4-6}{4-0}\\\\m=\frac{-10}{4}\\\\m=-\frac{5}{2}$

Now, the y-intercepts:

Line 1: -2

Line 2: 6

Write the equations:

Line 1: $y=\frac{1}{2}x-2$

Line 2: $y=-\frac{5}{2}x+6$

7)

A system with 1 solution means 2 lines that intersect at 1 point. Problems 5 and 6 are both examples of this. A system with no solution means lines that never intersect, meaning that they have the same slope, they're parallel.

Example:

$y=2x+1\\y=2x+2$

Those both have a slope of 2, and if you graph them, you'll see that they never intersect.

A system with infinitely many solutions means they intersect at every possible point. These would just be the same line.

Example:

$y=2x+1\\y=2x+1$

That's what they are, graph them however you like.