Let f(x) = x+1 and g(x) = -(1/5)x +3
How can we find the size of angles formed by these two lines
Did you know that the slope of a line is the tangent of the angle that this line makes with the x-axis ?
so the slope of y = x+1 is 1, so it makes a 45° angle with the x-axis ( inverse tan(1) = 45)
the second line has slope -1/5, so it makes an angle of 168.69°
so the angle between the lines is 168.69-45 or 123.69°
Let f(x) = x+1 and g(x) = -(1/5)x +3
How can we find the size of angles formed by these two lines
To find the size of angles formed by two lines, you need to determine the slope of each line and then use the properties of angles formed by intersecting lines.
First, let's find the slopes of the lines. The given functions f(x) = x + 1 and g(x) = -(1/5)x + 3 are linear functions in the form of y = mx + c, where m represents the slope of the line.
For f(x), the coefficient of x is 1, so the slope is 1. Therefore, the slope of f(x) is 1.
For g(x), the coefficient of x is -1/5, so the slope is -1/5. Therefore, the slope of g(x) is -1/5.
Since we have determined the slopes of both lines, we can now calculate the size of the angles formed by these lines.
The angle between two lines is equal to the absolute difference between their slopes. So, the size of the angle formed by the two lines is equal to |slope of f(x) - slope of g(x)|.
Let's substitute the slopes we found earlier into the formula:
|1 - (-1/5)| = |1 + 1/5|
Simplifying this expression:
|6/5| = 6/5
The size of the angle formed by the lines f(x) = x + 1 and g(x) = -(1/5)x + 3 is 6/5.