To determine the size of the acute angle created by the intersection of two lines, we need to find the slopes of the lines and calculate the angle between them.
Given two lines:
Line 1: y = 0.5x + 6
Line 2: y = -0.75x - 1
Step 1: Find the slopes of the lines.
The slopes of the lines can be found by inspecting the coefficients of x in their respective equations. Line 1 has a slope of 0.5, and Line 2 has a slope of -0.75.
Step 2: Calculate the angle between the lines.
The angle between two lines can be calculated using the formula:
angle = arctan |(m1 - m2) / (1 + m1 * m2)|
where m1 and m2 are the slopes of Line 1 and Line 2, respectively.
Plugging in the slopes we found earlier:
angle = arctan |(0.5 - (-0.75)) / (1 + (0.5 * -0.75))|
Now we can plug this into a calculator or use a trigonometric table to find the arctan of the value:
angle = arctan |(1.25) / (1 - 0.375)|
Simplifying:
angle = arctan |(1.25) / (0.625)|
angle = arctan(2)
Using a calculator, we find:
angle ≈ 63°
Therefore, the acute angle created by the intersection of the two lines is approximately 63 degrees.