Find the tangent of the angle in between the lines 2x+3y-5=0 and 5x=7y+3?

-29/31

Step-by-step explanation:

We are given;

The equations;

2x+3y-5=0 and 5x=7y+3

We are required to determine the tangent of the angle between the two lines;

We need to know that;

When an equation is written in the form of, y = mx + c

Then, tan θ = m, where θ is the angle between the line and the x-axis.

Therefore, we can find the tangent of the angle between each line given and the x-axis.

2x+3y-5=0

we first write it in the form, y = mx + c

We get, y = - 2/3x + 5/3

Thus, tan θ₁ = - 2/3

5x=7y+3

In the form of y = mx + c

We get; y = 5/7x - 3/7

Thus, tan θ₂ = 5/7

Using the formula, θ = tan^-1 ((m1-m2) / (1+m1m2)), where θ is angle between the two lines.

Thus, the tangent of the angle between the two lines will be;

tan θ = ((m1-m2) / (1+m1m2))

= ((-2/3-5/7) / (1 + (-2/3 * 5/7)))

= - 29/21 : 31/21

= - 29/31

Thus, the tangent of the angle between the two lines is - 29/31