Explanation And Solution For "Find The Missing Coordinate 1 For 3X 4Y 11"

[Solved] 1.Findthe missing coordinate (? , 1) for 3x 4y = 11 2 from www.coursehero.com

Understanding Coordinate Planes

Before we dive into finding the missing coordinate 1 for 3x 4y 11, let's first understand what a coordinate plane is. A coordinate plane is a two-dimensional plane that is divided into four quadrants. It is used to graph points and represent geometric figures. In a coordinate plane, the horizontal line is called the x-axis, and the vertical line is called the y-axis. The point where the two axes intersect is called the origin, and it is represented by the coordinates (0, 0). Points on a coordinate plane are represented by ordered pairs (x, y), where x is the coordinate on the x-axis and y is the coordinate on the y-axis.

Finding the Missing Coordinate

Now, let's move on to finding the missing coordinate 1 for 3x 4y 11. We have an equation 3x + 4y = 11, and we need to find the value of x or y when one of the coordinates is missing. To do this, we need to understand that the coordinates on the x-axis and y-axis are independent of each other. This means that if we know the value of one coordinate, we can find the value of the other coordinate using the equation. Let's say we know the value of x, and we want to find the value of y. We can rearrange the equation to solve for y: 4y = 11 - 3x y = (11 - 3x)/4 Similarly, if we know the value of y, we can find the value of x by rearranging the equation: 3x = 11 - 4y x = (11 - 4y)/3

Example

Let's take an example to understand this better. We have an equation 3x + 4y = 11, and one of the coordinates is missing. Let's say we know that y = 2. To find the missing coordinate, we can substitute y = 2 in the equation and solve for x: 3x + 4(2) = 11 3x + 8 = 11 3x = 3 x = 1 Therefore, the missing coordinate in the ordered pair (x, y) is x = 1. The ordered pair is (1, 2).

Graphing the Equation

We can also graph the equation 3x + 4y = 11 to find the missing coordinate. To graph the equation, we need to find at least two points on the line. Let's choose x = 0 and y = 0 to find the intercepts on the x-axis and y-axis, respectively. When x = 0, we get: 3(0) + 4y = 11 y = 11/4 Therefore, the point on the line is (0, 11/4). When y = 0, we get: 3x + 4(0) = 11 x = 11/3 Therefore, the point on the line is (11/3, 0). We can now plot these two points on the coordinate plane and draw a straight line passing through them. To find the missing coordinate, we can look at the graph and see which point is missing either x or y. In our example, we know that y = 2. Therefore, the missing coordinate is x. We can draw a vertical line passing through the point (2, 0) and see where it intersects the line. The x-coordinate of the intersection point is the missing coordinate.

Conclusion

In conclusion, finding the missing coordinate in an equation is easy once we understand how to rearrange the equation and solve for the missing coordinate. We can also graph the equation to find the missing coordinate by looking at the axis where the coordinate is missing and drawing a line passing through the known point.