Explanation:
To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:
m = (9 - 2) / (8 - (-2))
= 7 / 10
= 0.7
The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:
tan(θ) = 0.7
Taking the inverse tangent of both sides, we find:
θ = arctan(0.7)
Using a calculator, we can evaluate this to be approximately:
θ ≈ 35.87 degrees
Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.