Question

What equation had a slope of -1 and a y-intercept of 5

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equation with a slope of -1 and a y-intercept of 5 can be written in slope-intercept form as:

y = -x + 5

Answer 2

Graph y=1/2x+2 and y=-1/4x+8 then find the solution

Answer 3

[AI-generated answer — Bot GPT 3.5]

To graph the equations y = 1/2x + 2 and y = -1/4x + 8, we can plot a few points for each equation and then draw the lines.

For y = 1/2x + 2:
When x = 0, y = 2
When x = 2, y = 3
When x = -2, y = 1

Plotting these points we can draw the line:

```
|
10| *
|
| *
|
| *
|
|*
|
|
|______________
-10 -5 0 5 10
```

For y = -1/4x + 8:
When x = 0, y = 8
When x = 4, y = 7
When x = -4, y = 9

Plotting these points we can draw the line:

```
|
10|
|
|
|
|
|*
|
| *
|
| *
|
|
|______________
-10 -5 0 5 10
```

To find the solution, we need to find the point where the two lines intersect. From the graph, it appears that they intersect near (4, 7).

Answer 4

There's only two points

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion. You are correct. Let's find the solution algebraically by setting the two equations equal to each other and solving for x.

1/2x + 2 = -1/4x + 8

To eliminate the fractions, we can multiply both sides of the equation by the common denominator, which is 4:

4 * (1/2x + 2) = 4 * (-1/4x + 8)
2x + 8 = -x + 32

Next, let's move the -x term to the left side and the 8 term to the right side:

2x + x = 32 - 8
3x = 24

Now, divide both sides of the equation by 3:

x = 24/3
x = 8

Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the first equation:

y = 1/2(8) + 2
y = 4 + 2
y = 6

Therefore, the solution to the system of equations is (8, 6) which means the two lines intersect at the point (8, 6).

Answer 6

Find both points please

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. To find both points where the two lines intersect, we'll continue solving the system of equations.

The two equations are:
1) y = 1/2x + 2
2) y = -1/4x + 8

Since both equations are equal to y, we can set them equal to each other:

1/2x + 2 = -1/4x + 8

To eliminate the fractions, we can multiply both sides of the equation by 4:

4 * (1/2x + 2) = 4 * (-1/4x + 8)
2x + 8 = -x + 32

Next, let's move the -x term to the left side and the 8 term to the right side:

2x + x = 32 - 8
3x = 24

Now, divide both sides of the equation by 3:

x = 24/3
x = 8

Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the first equation:

y = 1/2(8) + 2
y = 4 + 2
y = 6

So the first point where the two lines intersect is (8, 6).

Let's substitute x = 8 into the second equation to find the value of y:

y = -1/4(8) + 8
y = -2 + 8
y = 6

So the second point where the two lines intersect is also (8, 6).

Therefore, the two lines intersect at the points (8, 6) and (8, 6).