Coordinate plane has a rectangular axes where the horizontal line represent the x values and vertical lines represent the y values. We can work out two concurrent equations in x and y by representation of graphs corresponding to the equations. An equation in x and y is in the form of $a x + b y + c = 0$. The equation correspond to a straight line, so, the problem of solving two concurrent equations in x and y decreases to the problem of finding the familiar point stuck between the two corresponding lines. To graph an equation on the coordinate plane we need a set of coordinates falling on the curve of the given equation. Joining the dots the curve can be completed.
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Following steps are used for graphing coordinate plane:
In graphing, to plot graph on a plane. Basically, we need two axes as x-axis and y-axis compulsory.
In a plane x-axis value is zero for y, in y-axis x value is zero.
The given steps are used to plot the graph for a line equation in a plane.
Step 1: Put few different values of x in the equation y = f(x) and get the corresponding values of y. Hence, different (x, y) values are obtained. Also, find the value of y at x = 0, and value of x at y = 0 to obtain the intercepts.
Step 2: Draw coordinate plane and mark the points on both the axes on equal intervals.
Step 3: Plot the obtained coordinate points on the plane drawn.
Step 4:Join the points to graph the curve.
Examples to graphing on a coordinate plane are as follows:
Example 1: Draw the graph y = 2x - 5.
Solution:Substituting x = -1, 0.5, 1, 2 in the equation of the line, we get y = -7, -4, -3, -1 equivalently. In a graph, plot the
Points (-1, -7), (0.5, -4), (1, -3), (2, -1)
Link the points by a line fragment and lengthen it in each direction. Thus we obtain the linear graph solution.
Example 2: Draw the graph of the line 2x + y = 7.
Solution: The given equation is rewritten as y = 7 - 2x.
Substituting x = -1 then y = 7 - (-2) = 9.
x = 0, then y = 7
x = 2 then y = 7 - 4 = 3.
Plot x and y values in the graph sheet. [(-1, 9), (0, 7) and (1, 3)]
Link the points by a line fragment and expand it in both the ways. Thus we obtain the linear graph solution.
1. Draw the graph of the following: y = 3x - 1
2. Draw the graph of the line equations: 3y + 2x - 12 = 0.
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