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 coordinates 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 coordinates of the point where the two lines intersect.
(ii) the area of the triangle between the lines and the x-axis.

KnowledgeBoat · Accepted Answer

(i) Given, ⇒ 6y = 5x + 10 ⇒ y = .........(1) When x = 1, y = = 2.5 x = -2, y = = 0, x = 4, y = = 5. Table of values of equation (1) : x | 1 | -2 | 4 ---- | ---- | ---- | ---- y | 2.5 | 0 | 5 Steps of construction : 1. Plot the points (1, 2.5), (-2, 0) and (4, 5) on graph. 2. Join the points. Given, y = 5x - 15 When x = 2.5, y = 5 × 2.5 - 15 = 12.5 - 15 = -2.5, x = 3, y = 5 × 3 - 15 = 15 - 15 = 0, x = 4, y = 5 × 4 - 15 = 20 - 15 = 5. Table of values of equation (2) : x | 2.5 | 3 | 4 ---- | ---- | ---- | ---- y | -2.5 | 0 | 5 Steps of construction : 1. Plot the points (2.5, -2.5), (3, 0) and (4, 5) on graph. 2. Join the points. From graph, The lines intersect at point P(4, 5). Hence, x = 4, y = 5. (ii) From graph, Triangle = PQR. Draw a line PJ, from P perpendicular to x-axis. PJ = 5 units QR = 5 units Area of triangle = × base × height = × QR × PJ = × 5 × 5 = = 12.5 sq. units. Hence, area = 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 coordinates of the point where the two lines intersect.
(ii) the area of the triangle between the lines and the x-axis.

Coordinate Geometry

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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 coordinates of the point where the two lines intersect.(ii) the area of the triangle between the lines and the x-axis.

Coordinate Geometry

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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 coordinates of the point where the two lines intersect.
(ii) the area of the triangle between the lines and the x-axis.

Solve the following system of equations graphically :
x - 2y - 4 = 0, 2x + y - 3 = 0.

Find, graphically, the coordinates of the vertices of the triangle formed by the lines:
8y - 3x + 7 = 0, 2x - y + 4 = 0 and 5x + 4y = 29.