The equation with a slope of -1 and a y-intercept of 5 can be written in slope-intercept form as:
y = -x + 5
What equation had a slope of -1 and a y-intercept of 5
7 answers
Graph y=1/2x+2 and y=-1/4x+8 then find the solution
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:
```
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10| *
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| *
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| *
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|*
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|
|______________
-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).
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).
There's only two points
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).
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).
Find both points please
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).
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).