graph y=-1/2x-6 and y=7/6x+7 using 2 plots
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
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
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
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
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).