graph and then find the solution for y=-1/2x-6 and y=7/6x+7
use 2 points on the graph
To graph the two equations, y = -1/2x - 6 and y = 7/6x + 7, we can plot a few points and then connect them to form lines.
For the first equation y = -1/2x - 6:
To find points on this line, we can assign values to x and then solve for y.
For x = 0, we have y = -1/2(0) - 6 = -6. So, one point is (0, -6).
For x = 2, we have y = -1/2(2) - 6 = -1 - 6 = -7. So, another point is (2, -7).
Plotting these two points and drawing a line passing through them, we have the graph of y = -1/2x - 6.
For the second equation y = 7/6x + 7:
For x = 0, we have y = 7/6(0) + 7 = 0 + 7 = 7. So, one point is (0, 7).
For x = 6, we have y = 7/6(6) + 7 = 7 + 7 = 14. So, another point is (6, 14).
Plotting these two points and drawing a line passing through them, we have the graph of y = 7/6x + 7.
The graphs of y = -1/2x - 6 (represented by the blue line) and y = 7/6x + 7 (represented by the red line) intersect at one point. The solution to the system of equations is the coordinates of the point of intersection.
Let's find the point of intersection:
Setting the two equations equal to each other, we have:
-1/2x - 6 = 7/6x + 7
To solve for x, we can start by multiplying both sides of the equation by 6 to eliminate the fractions:
-3x - 36 = 7x + 42
Next, we can combine like terms:
-3x - 7x = 42 + 36
-10x = 78
Dividing both sides of the equation by -10, we get:
x = 78/-10
x = -7.8
Now, substitute x = -7.8 into either of the original equations to find y. Let's use the first equation:
y = -1/2(-7.8) - 6
y = 3.9 - 6
y = -2.1
Therefore, the solution to the system of equations is (-7.8, -2.1).
Here is the graph: 