Using the intersection method, I need to solve the following equation:
5x-3.3=x-2.1
Can you point me on the right path?
you have to get x's on one side, and the numbers on the other.
then solve for x.
Kira,
Thank so much for your help, but how do you graph the equation to solve? I am not sure which part of the equation is along the x axis and which part goes along the y?
A.tgmgtgtgmgtg
To solve the equation using the intersection method, you don't necessarily need to graph it, but I can explain how to do so if that helps you visualize it better.
First, rearrange the equation by combining like terms. Move the x terms to one side of the equation and the numerical terms to the other side. In this case, subtract x from both sides and add 3.3 to both sides:
5x - x = 2.1 + 3.3
Simplifying, we get:
4x = 5.4
Now, divide both sides of the equation by 4 to isolate x:
x = 5.4 / 4
Simplifying further, we have:
x = 1.35
So the solution to the equation is x = 1.35.
Now, if you want to graph the equation, note that the equation you have is a linear equation. To graph it, you can plot two points on the coordinate plane and draw a straight line passing through those points.
For example, you can choose two values for x and calculate the corresponding values for y. Let's choose x = 0 and x = 2:
For x = 0:
5(0) - 3.3 = 0 - 2.1
-3.3 = -2.1
For x = 2:
5(2) - 3.3 = 2 - 2.1
6.7 = -0.1
The points we obtain from these calculations are (0, -3.3) and (2, 6.7). Plot these points on the coordinate plane, and draw a straight line passing through them. The x-axis represents the x-values, and the y-axis represents the y-values.
Alternatively, you can rearrange the equation in slope-intercept form (y = mx + b) and graph it directly. In this case, solving for y, we have:
5x - 3.3 = x - 2.1
4x = 1.2
x = 0.3
Now substitute this value of x back into the equation to find y:
y = 5(0.3) - 3.3
y = 1.5 - 3.3
y = -1.8
So the equation in slope-intercept form is y = 5x - 1.8. From this form, you can identify the slope (5) and the y-intercept (-1.8), allowing you to graph the line.
Remember, graphing the equation is not necessary to find the solution. It is an additional tool that can help you visualize the relationship between x and y.