graph y=-1/2x-6 and y=7/6x+7 using 2 plots
![Bot GPT 3.5](/images/users/4310/128x128.jpeg)
To plot the graph of y = -1/2x-6, we can start by choosing some x-values and finding the corresponding y-values.
Let's choose three values of x: x = -4, 0, and 4.
When x = -4:
y = -1/2(-4) - 6
y = 2 - 6
y = -4
When x = 0:
y = -1/2(0) - 6
y = 0 - 6
y = -6
When x = 4:
y = -1/2(4) - 6
y = -2 - 6
y = -8
So, our first set of coordinates is (-4, -4), (0, -6), and (4, -8).
Now, let's plot these points on the graph:
Coordinates: (-4, -4), (0, -6), and (4, -8)
Now, let's plot the graph of y = 7/6x+7 using the same method.
Let's choose the same values of x as before: x = -4, 0, and 4.
When x = -4:
y = 7/6(-4) + 7
y = -28/6 + 7
y = -28/6 + 42/6
y = 14/6
y = 7/3
When x = 0:
y = 7/6(0) + 7
y = 0 + 7
y = 7
When x = 4:
y = 7/6(4) + 7
y = 28/6 + 7
y = 28/6 + 42/6
y = 70/6
y = 35/3
So, our second set of coordinates is (-4, 7/3), (0, 7), and (4, 35/3).
Now, let's plot these points on the graph:
Coordinates: (-4, 7/3), (0, 7), and (4, 35/3)
2 points only
![Bot GPT 3.5](/images/users/4310/128x128.jpeg)
Sure! Let's choose two points to plot for each equation.
For equation y = -1/2x - 6:
When x = -4:
y = -1/2(-4) - 6
y = 2 - 6
y = -4
When x = 4:
y = -1/2(4) - 6
y = -2 - 6
y = -8
The two points for this equation are (-4, -4) and (4, -8).
For equation y = 7/6x + 7:
When x = -4:
y = 7/6(-4) + 7
y = -28/6 + 7
y = -4 + 7
y = 3
When x = 4:
y = 7/6(4) + 7
y = 28/6 + 7
y = 4 + 7
y = 11
The two points for this equation are (-4, 3) and (4, 11).
Now, let's plot these two points on the graph.
where do they intersect
![Bot GPT 3.5](/images/users/4310/128x128.jpeg)
To find the point of intersection between the two equations, we can set them equal to each other and solve for x.
-1/2x - 6 = 7/6x + 7
First, let's multiply everything by 6 to remove the fractions:
-3x - 36 = 7x + 42
Add 3x to both sides:
-36 = 10x + 42
Subtract 42 from both sides:
-78 = 10x
Divide by 10:
-7.8 = x
Now substitute this value into either equation to find the y-coordinate:
y = -1/2x - 6
y = -1/2(-7.8) - 6
y = 3.9 - 6
y = -2.1
So the point of intersection is approximately (-7.8, -2.1).
graph y=-1/2x-6 and y=7/6x+7 using 2 points and find the solution
![Bot GPT 3.5](/images/users/4310/128x128.jpeg)
To graph the equations y = -1/2x - 6 and y = 7/6x + 7, we will use two points for each equation.
For the first equation, y = -1/2x - 6:
When x = 0:
y = -1/2(0) - 6
y = 0 - 6
y = -6
When x = 4:
y = -1/2(4) - 6
y = -2 - 6
y = -8
So, the two points for the first equation are (0, -6) and (4, -8).
For the second equation, y = 7/6x + 7:
When x = 0:
y = 7/6(0) + 7
y = 0 + 7
y = 7
When x = 4:
y = 7/6(4) + 7
y = 28/6 + 7
y = 28/6 + 42/6
y = 70/6
y = 35/3
So, the two points for the second equation are (0, 7) and (4, 35/3).
Now let's plot these points on a graph:
- First equation points: (0, -6) and (4, -8)
- Second equation points: (0, 7) and (4, 35/3)
Graph:
graph y=-1/2x-6 and y=7/6x+7 using 2 points
find the solution to y=-1/2x-6 and y=7/6x+7
![Bot GPT 3.5](/images/users/4310/128x128.jpeg)
To find the solution for the equations y = -1/2x - 6 and y = 7/6x + 7, we need to find the x-value where the two equations intersect.
First, let's set the two equations equal to each other:
-1/2x - 6 = 7/6x + 7
To solve for x, let's clear the fractions by multiplying every term by the least common denominator, which is 12:
12*(-1/2x - 6) = 12*(7/6x + 7)
-6x - 72 = 14x + 84
Next, let's combine like terms:
-6x - 14x = 84 + 72
-20x = 156
Divide both sides by -20:
x = 156/-20
Simplifying the fraction:
x = -39/5
Now, substitute this value back into either of the original equations to find the y-value.
Let's use the equation y = -1/2x - 6:
y = -1/2(-39/5) - 6
y = 39/10 - 60/10
y = (39 - 60)/10
y = -21/10
So, the solution to the equations y = -1/2x - 6 and y = 7/6x + 7 is approximately (-39/5, -21/10) or (-7.8, -2.1).