To graph the systems of equations y = -1/4x + 3 and y = 3/4x - 1, we can start by finding the x and y coordinates of the intersection points. The intersection points are the points that satisfy both equations, meaning the x and y coordinates are equal. To find the intersection points, we can set the two equations equal to each other and solve for x.
-1/4x + 3 = 3/4x - 1
Multiplying both sides by 4 to get rid of the fraction:
-4x + 12 = 3x - 4
Adding 4x and -4 to both sides:
0 = 7x - 8
Adding 8 to both sides:
8 = 7x
Dividing both sides by 7:
x = 8/7
Now that we have found the x-coordinate, we can use either equation to find the corresponding y-coordinate. For example, using the first equation:
y = -1/4x + 3
y = -1/4 * (8/7) + 3
y = -1/4 * 8/7 + 21/7
y = -2/7 + 21/7
y = 19/7
So, the intersection point is (8/7, 19/7).
Next, we can plot the two lines and the intersection point on the coordinate plane. To do this, we can choose several x values and substitute them into the two equations to find the corresponding y values. Then, we can plot the points and connect them with lines to form the two lines. The intersection point is where the two lines meet.
The final graph would look something like this:
[Insert graph of two lines and intersection point]
This graph represents the solutions to the systems of equations y = -1/4x + 3 and y = 3/4x - 1. Any point that lies on both lines would be a solution to the system, meaning the x and y coordinates would satisfy both equations. The intersection point represents the unique solution where both lines meet