How do you solve this algebraic equation using graphing?
y = 3x - 1
y = -x + 1
y = 3x - 1
y = -x + 1
Find points for each equation, then plot the points for each, draw a line connecting these points for each equation.
The point of intersection is the solution.
y = 3x - 1
x = 0, y = -1
x = -1, y = -4
x = 1, y = 2
x = 1/2, y = 1/2
So, you would plot the points,
(0,-1), (-1,-4), (1,2), (1/2, 1/2) and draw a line through these points.
y = -x + 1
x = 0, y = 1
x = -1, y = 2
x = 1, y = 0
x = 1/2, y = 1/2
Plot the points,
(0,1), (-1,2), (1,0)
and draw a line through these points.
The point of intersection is the solution. The P(x,y) will satisfy both equations.
To solve the algebraic equation using graphing, follow these steps:
Step 1: Start by plotting the graph of each equation.
First equation: y = 3x - 1
To graph this equation, choose a few values for x and calculate the corresponding y values. For example, let's choose x = 0, x = 1, and x = -1.
When x = 0, y = 3(0) - 1 = -1. This gives us the point (0, -1).
When x = 1, y = 3(1) - 1 = 2. This gives us the point (1, 2).
When x = -1, y = 3(-1) - 1 = -4. This gives us the point (-1, -4).
Plot these points on a coordinate plane, and then draw a straight line passing through these points. This line represents the graph of the first equation.
Second equation: y = -x + 1
Repeat the process with the second equation. Choose different values for x and calculate the corresponding y values. For example, let's choose x = 0, x = 1, and x = -1.
When x = 0, y = -(0) + 1 = 1. This gives us the point (0, 1).
When x = 1, y = -(1) + 1 = 0. This gives us the point (1, 0).
When x = -1, y = -(-1) + 1 = 2. This gives us the point (-1, 2).
Plot these points on the same coordinate plane and draw a straight line passing through these points. This line represents the graph of the second equation.
Step 2: Find the point of intersection.
The solution to the system of equations is the point where the two graphs intersect. Locate the point where the two lines intersect on the graph.
Step 3: Determine the coordinates of the intersection point.
Once you locate the point of intersection, read the coordinates from the graph. The x-coordinate and y-coordinate of the intersection point represent the solution for the system of equations.
That's it! You have solved the algebraic equation using graphing.