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

tanФ = 2.6363636

Step-by-step explanation:

To find the tangent of the angle in-between the lines we will follow the steps below:

We are going to use the formula;

tanФ = |m₂ - m₁  / 1 + m₁m₂|

We can get the slope m₁ from the first equation

2x+3y–5=0

we will re-arrange it in the form y=mx + c

3y = -2x + 5

Divide through by 3

y = -x +

comparing the above equation with y=mx + c

m₁ =  -

We will proceed to find the second slope m₂ using the second equation

5x=7y+3

we will re-arrange it in the form y=mx + c

7y = 5x -3

divide through by 7

y = x -  

comparing the above with y=mx + x

m₂ =

we can now go ahead and substitute into the formula

tanФ = |m₂ - m₁  / 1 + m₁m₂|

tanФ = | -  (- ) / 1 +  (-₁)( )|

tanФ = | +  / 1 -  |

tanФ = | / |

tanФ = | × |

21 will cancel-out 21

tanФ =

tanФ = 2.636363

answer: 5

step-by-step explanation: