Question

find the equation of a straight line which makes double at the x intercept and triple at the y intercept made by the line 4x+5y=20 on the axes​

Answer 1

• 
  `y = - ( \frac { 6}{5} )x + 12 \\`

Task :

• To work out the equation of a straight line which makes 2x at the x intercept and 3x at the y intercept made by the line given ( 4x + 5y = 20)

Solution :

Firstly,we will find the x and y intercepts of the given line equation by setting the opposite variable zero.

x-intercept

• 4x + 5(0) = 20
• 4x = 20
• x = 5
• x-intercept = (5,0)

y-intercept

• 4(0) + 5y = 20
• 5y = 20
• y = 4
• y-intercept = (0,4)

ATQ,

• y'-intercept : 3(0,4) =(0,12)
• x'-intercept : 2(5,0) =(10,0)

Now,

We'll find the slope of the new line using the formula :

• 
  `m = (∆y)/(∆x) \\`

Plugging in the values,

• 
  `m = ((0 - 12))/((10 - 0)) = ( - 12)/(10) = ( - 6)/(5) \\`

Thus, the slope of the new straight line is -6/5.

Now, since we have the slope(-6/5) and x-intercept (10,0) ,we can easily find the equation of the straight line by using the point-slope form of the equation that is given by :

• 
  `y - y_1 = m(x - x_1)`

Plugging in the values,

• 
  `y - 0 = ( - 6)/(5) (x - 10) \\`
• 
  `y = ( - (6)/(5) )x - ( - (6)/(5) * 10) \\`
• 
  `y = - ( \frac { 6}{5} )x + 12 \\`

Thus, the required equation of a straight line which makes double at the x intercept and triple at the y intercept is y = -(6/5)x + 12.

Answer 2

`\sf y = -(6)/(5)x + 12`

Explanation:

In order t find the equation of the line which makes double at the x intercept and triple at the y intercept made by the line 4x+5y=20 on the axes, we can use the following steps:

• Find the x and y intercepts of the line 4x+5y=20.
• Double the x intercept and triple the y intercept.
• Find the equation of the line that passes through the doubled x intercept and tripled y intercept.

Step 1: Find the x and y intercepts of the line 4x+5y=20.

To find the x intercept, we set y to 0 and solve for x.

4x + 5(0) = 20

4x = 20

x = 5

To find the y intercept, we set x to 0 and solve for y.

4(0) + 5y = 20

5y = 20

y = 4

Therefore, the x intercept of the line 4x+5y=20 is (5,0) and the y intercept is (0,4).

Step 2: Double the x intercept and triple the y intercept.

The doubled x intercept is (10,0) and the tripled y intercept is (0,12).

Step 3: Find the equation of the line that passes through the doubled x intercept and tripled y intercept.

The slope of the line that passes through (10,0) and (0,12) is:

`\sf m = \frac{\textsf{ Change in y }}{\textsf{ Change in x}} \\\\ = ((12 - 0) )/( (0 - 10) )\\\\ = -(6)/(5)`

The equation of the line that passes through (10,0) with a slope of -6/5 is:

`\sf y - 0 = -(6)/(5)(x - 10)`

`\sf y = -(6)/(5)x + 12`

Therefore, the equation of the line which makes double at the x intercept and triple at the y intercept made by the line 4x+5y=20 on the axes is:

`\sf y = -(6)/(5)x + 12`