Given the interval 0<θ<π/2. Find the angle θ which is formed by the line y = -2x+4 and y = 3x-3 Show your work as well, thank you!​

Step-by-step explanation:

we want to find the acute angle θ (as θ is between (0,π/2)) formed by the line y=-2x+4 and y=3x-3 to do so we can consider the following formula:

From the first equation we obtain that is -2 and from the second that is 3 therefore substitute:

simplify multiplication:

simplify Parentheses:

simplify addition:

simplify division:

calculate the absolute of -1:

calculate the inverse function:

hence,

the angle θ which is formed by the line y = -2x+4 and y = 3x-3 is π/4

(for more info about the formula refer the attachment thank you!)