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
