Determine the angle between the two lines with equations 4x - 5y = 11 and 2x + 3y = 7.

The angle between the two lines is 72.35° ⇒ to the nearest hundredth

Step-by-step explanation:

The angle between the two lines is the difference between their angles with the positive part of the x-axis (Ф = Ф - Ф) The slope of the line equal to the tangent of the angle between the line and the positive part of the x-axis (m = tan Ф)The slope of the line whose equation is ax + by = c is m =

∵ The equation of the first line is 4x - 5y = 11

∴ a = 4 and b = -5

→ By using the 3rd rule of the slope above

∵ m = =

∴ m = 0.8

→ By using the 2nd rule above

∵ tan Ф = 0.8

∴ Ф = (0.8)

∴ Ф = 38.66° ⇒ to the nearest hundredth

∵ The equation of the first line is 2x + 3y = 7

∴ a = 2 and b = 3

→ By using the 3rd rule of the slope above

∵ m =

∴ m =

→ By using the 2nd rule above

∵ tan Ф =  

∴ Ф = ( )

∴ Ф = -33.69° ⇒ to the nearest hundredth

→ By using the 1st rule above

∵ Ф = -33.69 - 38.66

∴ Ф = -72.35°

→ Ignore the negative sign

∴ The angle between the two lines is 72.35° ⇒ to the nearest hundredth

V.I.N:

You can use this rule to find the angle between 2 lines tan Ф = II

(x+7)÷5

Step-by-step explanation:

since the number is unknown, it becomes X. Because we first add 7 then divide by 5, the expression will be a bracketed (X+7), followed by the division by 5. This makes sense because of the BODMAS rule to which, in coherence with the BODMAS rule, we first solve the expression in the brackets then move on outside them.