Question

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

Answer 1

Answer:

-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