Question

For a equation 3 x minus 5 Y - 15 is equal to zero find the point where its graph intersect x-axis and y-axis using these draw the graph of the equation and find its area

Answer 1

Question:

fthe equation 3x - 5y -15 = 0 , find the point where its graph intersects x-axis and y-axis.Using these draw the graph of the equation and find the area bounded by x-axis, y-axis and the given line.

Note:

x,y-intercept form of the straight line;

The equation of a straight line in x,y-intercept form is given by:

x/a + y/b = 1

where;

a is the x-intercept and

b is the y-intercept.

Solution:

Here,

The given equation of straight line is;

=> 3x - 5y -15 = 0

=> 3x - 5y =15

=> 3x/15 - 5y/15 = 1

=> x/5 - y/3 = 1

=> x/5 + y/(-3) = 1

Hence,

The x,y-intercept form of the given straight line is; x/5 + y/(-3) = 1.

Here,

The x-intercept and y-intercept of given straight line are 5 and -3 respectively.

Also;

Point of intersection on x-axis will be;

(5,0) and

Point of intersection on y-axis will be;

(0,-3)

Also,

The area of the region bounded by x-axis, y-axis and the straight line is given by ;

Area = |(x-intercept)•(y-intercept)|/2

Clearly,

For the given straight line , we have;

x-intercept = 5 and

y-intercept = - 3

Hence,

The area of the region bounded by x-axis, y-axis and the given straight line will be;

Area = |5•(- 3)|/2

= | - 15|/2

= 15/2

= 7.5 sq. units