The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree
Step-by-step explanation:
The formula to find the angle between the positive part of x-axis and a line y = m x + b is tan(Ф) = m, where
- Ф is the angle between the line and the positive part of x-axis
- m is the slope of the line
∵ The equation of the line is [tex]y=\frac{5}{4}x[/tex]
∵ The form of the equation of a line is y = m x + b
∴ m = [tex]\frac{5}{4}[/tex] and b = 0
∵ Ф is the angle between the line and the positive part of x-axis
∵ tan(Ф) = m
∴ tan(Ф) = [tex]\frac{5}{4}[/tex]
- To find Ф use the inverse function of tan ( [tex]tan^{-1}[/tex]
∵ Ф = [tex]tan^{-1}(\frac{5}{4})[/tex]
∴ Ф = 51.34°
- Round it to the nearest degree
∴ Ф = 51°
The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree
Learn more:
You can learn more about the linear equation in brainly.com/question/1284310
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