Make and Draw linear graph
The coordinate graph is called as a Cartesian coordinate plane. The graph contains a couple of vertical lines called coordinate axes. The vertical axis y axis value and the horizontal axis value is the x axis value. The points of intersection of those two axes values are called the origin of coordinate graphing pictures. Moreover, point to a right of the origin on the x axis value and above the origin on the y axis represents positive real numbers. The points to the left of the origin value on the x axis or below the origin on the y axis represent negative real numbers. In this article we shall discuss about make linear graph.
A linear equation is an algebraic equation in the each terms is either a constant or the product of a constant and (the first power of) a single variable. Ax +By=C, where A, B, and C are integers whose greatest common factor is 1, A and B are not both equal to zero, and A is non-negative (and if A = 0 then B has to be positive). The standard form can be converted to the general forms, but not always to all the other forms if A or B is zero. (Source.Wikipedia)
Sample problem for make linear graph:
Problem 1:
Solve the given linear equation and make the graph y = 2x - 3.find the coordinate value of the vertex of a triangle formed by lines and the x axis in graph.
Solution:
Given:
We are find the points for the plotting the graph points using given linear equation.
In the equation we following terms,
Y = 2x - 3
In the above equation in the form of y = mx + c. In the above equation is equal to zero, we get
2 x – y - 3 = 0
2x = y + 3
Equation (1) is divided by -1. We get
-2x = -y - 3
y = 2x - 3 -------------- (1)
In the above equation we plot the points of y axis, for several x axis values. From equation (1) we get the following values
X -1 0 1 2
Y -5 -3 -1 3
Problem 2:
Solve the given linear equation and make the graph y = x - 8.find the coordinate value of the vertex of a triangle formed by lines and the x axis in graph.
Solution:
Given:
We find the points for the plotting the graph points using given linear equation.
In the equation we following terms,
Y = x - 8
In the above equation in the form of y = mx + c. In the above equation is equal to zero, we get
x – y – 8 = 0
x = y + 8
Equation (1) is divided by -1. We get
-x = -y - 8
y = x - 8 -------------- (1)
In the above equation we draw the points of y axis, for several x axis values. From equation (1) we get the following values
X -1 0 1 2
Y -9 -8 -7 -6
linear graph
Sample problem for draw linear graph:
Problem 1:
Solve the given linear equation and draw the graph y = 4x + 3.find the coordinate of vertex of triangle formed by lines and the x axis in graph.
Solution:
Given:
We find the points for plotting the graph using given linear equation.
In the equation we following terms,
Y = 4x + 3
In the above equation in the form of = mx + c. In the above equation is equal to zero, we get
4x – y + 3 = 0
4x = y - 3
Equation (1) is divided by -1. We get
-4x = -y + 3
y = 4x + 3 -------------- (1)
In the above equation we plot the points of y axis, for several x axis values. From equation (1) we get the following values
X -1 0 1 2
Y -1 3 7 10
graph
Problem 2: linear graph:
Solve the given linear equation and draw the graph y = 2x - 5.find the coordinate of vertex of triangle formed by lines and the x axis in graph.
Solution:
Given:
We find the points for plotting the graph using given linear equation.
In the equation we following terms,
Y = 2x - 5
In the above equation in the form of = mx + c. In the above equation is equal to zero, we get
2 x – y – 5 = 0
2x = y + 5
Equation (1) is divided by -1. We get
-2x = -y - 5
y = 2x - 5 -------------- (1)
In the above equation we draw the points of y axis, for several x axis values. From equation (1) we get the following values
X -1 0 1 2
Y -7 -5 -3 -1
Graph
Example 1:
Plot the linear graph of y = 5x + 2.
Solution:
Construct a table and choose simple x values.
In order to find the y values for the table, subsutitute each x vale into the rule y = 5x + 2
When x = -2 , y= 5(-2)+2
= -10+2
= -8
When x =-1, y = 5(-1) + 2
= -5+2
= -3
When x =0, y =3(0)+2
=0+ 2
= 2
When x =1,y=5(1)+2
= 5+2
= 7
When x =2, y=5(2)+2
= 10+2
= 12
Plots the points:
x -2 -1 0 1 2
y -8 -3 2 7 12
This point plot for required linear graph
Example 2:
A straight is expressed by the equation, 20x – 5y + 15 = 0.
Express the linear function in slope-intercept standard form of linear graph.
Solution:
20x – 5y + 15 = 0 or -5y = -20 x – 15 or y = 4x + 3
The slope-intercept form of the given equations is, y = 4x + 3
When x= -2 , y= 4(-2)+3
= -8+3
= -5
When x=-1, y = 4(-1) + 3
= -4+3
= -1
When x=0, y =3(0)+3
=0+ 3
= 3
When x=1,y=4(1)+3
= 4+3
= 7
When x =2, y=4(2)+3
= 8+3
= 13
plots the points:
x -2 -1 0 1 2
y -5 -1 3 7 13
4x-y-3 =0
This equation are called as standard form of linear equation graph