Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.
From the graph find :
(i) the co-ordinates of the point where the two lines intersect;
(ii) the area of the triangle between the lines and the x-axis.

Question

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.
From the graph find :
(i) the co-ordinates of the point where the two lines intersect;
(ii) the area of the triangle between the lines and the x-axis.

KnowledgeBoat · Accepted Answer

First equation: 6y = 5x + 10 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -8, then 6y = 5 (-8) + 10 ⇒ y = -5 Let x = -2, then 6y = 5 (-2) + 10 ⇒ y = 0 Let x = 4, then 6y = 5 4 + 10 ⇒ y = 5 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -8 | -2 | 4 --|--- |--- |--- y | -5 | 0 | 5 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. Second equation: y = 5x - 15 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = 3, then y = 5 3 - 15 ⇒ y = 0 Let x = 4, then y = 5 4 - 15 ⇒ y = 5 Let x = 5, then y = 5 5 - 15 ⇒ y = 10 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | 3 | 4 | 5 --|---|---|--- y | 0 | 5 | 10 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. (i) Both the straight line drawn meet at the point A. As it is clear from the graph, co-ordinates of the common point A are (4, 5). Hence, the co-ordinates of the point where the two lines intersect = (4, 5). (ii) The area of the triangle = x base x height = x BC x AD = x 5 x 5 = sq. units = 12.5 sq. units Hence, the area of the triangle between the lines and the x-axis = 12.5 sq. units.

Mathematics

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.
From the graph find :
(i) the co-ordinates of the point where the two lines intersect;
(ii) the area of the triangle between the lines and the x-axis.

Graphical Solution

Related Questions

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically :
(i) the area of triangle;
(ii) the co-ordinates of the vertices of the triangle.

By drawing a graph for each of the equations 3x + y + 5 = 0; 3y - x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point).
Take 2 cm = 1 unit on both the axes.

For the line 2x - y = 7 and for x = 3 the value of y is :
1
-1
5
-5

Mathematics

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.From the graph find :(i) the co-ordinates of the point where the two lines intersect;(ii) the area of the triangle between the lines and the x-axis.

Graphical Solution

Related Questions

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.Find, graphically :(i) the area of triangle;(ii) the co-ordinates of the vertices of the triangle.

By drawing a graph for each of the equations 3x + y + 5 = 0; 3y - x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point).Take 2 cm = 1 unit on both the axes.

For the line 2x - y = 7 and for x = 3 the value of y is :1-15-5

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.
From the graph find :
(i) the co-ordinates of the point where the two lines intersect;
(ii) the area of the triangle between the lines and the x-axis.

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically :
(i) the area of triangle;
(ii) the co-ordinates of the vertices of the triangle.

By drawing a graph for each of the equations 3x + y + 5 = 0; 3y - x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point).
Take 2 cm = 1 unit on both the axes.

For the line 2x - y = 7 and for x = 3 the value of y is :
1
-1
5
-5