Solve the equation 5x+7=13-7x graphically. then check your solution algebraically.
Looking at the graph, it appears that the intersection is at (1/2, 19/2).
Solving algebraically, we find
12x = 6
x = .5
y= 9.5
*what a surprise!*
To solve the equation 5x + 7 = 13 - 7x graphically, we need to plot the graphs of both sides of the equation on the coordinate plane and find the point of intersection.
Step 1: Write the equation in the form y = mx + b.
5x + 7 = 13 - 7x
=> 12x + 7 = 13
=> 12x = 13 - 7
=> 12x = 6
=> x = 1/2
Step 2: Plot the graph of 5x + 7.
To do this, assign different arbitrary values to x and calculate the corresponding y values.
x = 0, y = 7
x = 1, y = 12
x = 2, y = 17
Plot these points on the graph.
Step 3: Plot the graph of 13 - 7x.
Similarly, assign different values to x and calculate the corresponding y values.
x = 0, y = 13
x = 1, y = 6
x = 2, y = -1
Plot these points on the graph.
Step 4: Find the point of intersection.
The point where the two graphs intersect is the solution to the equation.
In this case, the point of intersection is (1/2, 7).
Now, let's check the solution algebraically.
Substitute x = 1/2 into the equation:
5(1/2) + 7 = 13 - 7(1/2)
=> 5/2 + 7 = 13 - 7/2
=> 5/2 + 14/2 = 26/2 - 7/2
=> 19/2 = 19/2
Since both sides of the equation are equal, the solution x = 1/2 is correct.
Therefore, the solution to the equation 5x + 7 = 13 - 7x is x = 1/2.