Introduction to solve graphing test:
Solve graphing test is one of interesting topics in mathematics. Without doing any algebraic manipulations, we can solve two simultaneous equations in x and y by drawing the graphs corresponding to the equations together. An equation in x and y is of the form a x + b y + c = 0. The equation represents a straight line, so, the problem of solving two simultaneous equations in x and y reduces to the problem of finding the common point between the two corresponding lines.
Steps to solve the graph:
The following steps are necessary to solve the graphing test:
Step 1:
Two different values are substitute for x in the equation y = mx + b, we get two values for y. Thus we get two points (x1, y1) and (x2, y2) on the line.
Step 2:
Draw the x-axis and y-axis on the graph and choose a suitable scale on the co- ordinate axes. Both the axes is chosen based on the scale values of the co-ordinates obtained in step 1. If the co-ordinate values are large in given data then 1 cm along the axes may be taken to represents large number of units.
Step 3:
Plot the two points (x1, y1) and (x2, y2) in Cartesian plane of the paper.
Step 4:
Two points are joined by a line segment and extend it in both directions of the segment. Then it is the required graph.
Examples to solve graphing test:
Examples to solve graphing test are as follows:
Example 1:
Draw the graph y = 3x −1.
Solution:
Substituting x = −1, 0, 1 in the equation of the line, we get y = −4, −1, 2 correspondingly. In a graph, plot the
Points (−1, −4), (0, −1) and (1, 2).
X -1 0 1
Y -4 -1 1
Join the points by a line segment and extend it in both directions. Thus we get the required linear graph
Example 2:
Draw the graph of the line 2x + 3y = 12.
Solution:
The given equation is rewritten as 3y = −2x + 12 or y = (−3 / 2)x + 4.
Substituting x = −3 then y = 6
x = 0, then y = 4
x = 3 then y = 2.
Plot x and y values in the graph sheet. [(−3, 6), (0, 4) and (3, 2)]
X -1 0 1
Y 5.5 4 2.5
Join the points by a line segment and extend it in both the directions. Then it is the required linear graph.
Practice problems to solve graphing test:
Some practice problems to solve graphing test
1. Draw the graph of the following : y = −2x
Answer: x -1 0 1
y 2 0 -2
2. Draw the graph of the following equations: y + 2x −5 = 0.
Answer: x -1 0 1
y 7 5 3
Solve graphing test is one of interesting topics in mathematics. Without doing any algebraic manipulations, we can solve two simultaneous equations in x and y by drawing the graphs corresponding to the equations together. An equation in x and y is of the form a x + b y + c = 0. The equation represents a straight line, so, the problem of solving two simultaneous equations in x and y reduces to the problem of finding the common point between the two corresponding lines.
Steps to solve the graph:
The following steps are necessary to solve the graphing test:
Step 1:
Two different values are substitute for x in the equation y = mx + b, we get two values for y. Thus we get two points (x1, y1) and (x2, y2) on the line.
Step 2:
Draw the x-axis and y-axis on the graph and choose a suitable scale on the co- ordinate axes. Both the axes is chosen based on the scale values of the co-ordinates obtained in step 1. If the co-ordinate values are large in given data then 1 cm along the axes may be taken to represents large number of units.
Step 3:
Plot the two points (x1, y1) and (x2, y2) in Cartesian plane of the paper.
Step 4:
Two points are joined by a line segment and extend it in both directions of the segment. Then it is the required graph.
Examples to solve graphing test:
Examples to solve graphing test are as follows:
Example 1:
Draw the graph y = 3x −1.
Solution:
Substituting x = −1, 0, 1 in the equation of the line, we get y = −4, −1, 2 correspondingly. In a graph, plot the
Points (−1, −4), (0, −1) and (1, 2).
X -1 0 1
Y -4 -1 1
Join the points by a line segment and extend it in both directions. Thus we get the required linear graph
Example 2:
Draw the graph of the line 2x + 3y = 12.
Solution:
The given equation is rewritten as 3y = −2x + 12 or y = (−3 / 2)x + 4.
Substituting x = −3 then y = 6
x = 0, then y = 4
x = 3 then y = 2.
Plot x and y values in the graph sheet. [(−3, 6), (0, 4) and (3, 2)]
X -1 0 1
Y 5.5 4 2.5
Join the points by a line segment and extend it in both the directions. Then it is the required linear graph.
Practice problems to solve graphing test:
Some practice problems to solve graphing test
1. Draw the graph of the following : y = −2x
Answer: x -1 0 1
y 2 0 -2
2. Draw the graph of the following equations: y + 2x −5 = 0.
Answer: x -1 0 1
y 7 5 3
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