Calculate, correct to one decimal place, the acute angle between the lines 3x - 4y + 5 = 0 and 2x + 3y - 1= 0.

70.6°

Step-by-step explanation:

The angle between the 2 lines can be calculated using

tanΘ = | | ( Θ is the angle between the lines )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange the 2 equations into this form to extract the slopes

3x - 4y + 5 = 0 ( subtract 3x + 5 from both sides )

- 4y = - 3x - 5 ( divide all terms by - 4 )

y = x + with m = ←

--------------------------------------------

2x + 3y - 1 = 0 ( subtract 2x - 1 from both sides )

3y = - 2x + 1 ( divide all terms by 3 )

y = - x + with m = - ←

Note it does not matter which slope is labelled or

Thus

tan Θ = |

          = | = | | = , then

Θ = ( ) ≈ 70.6° ( to 1 dec. place )