What is the inclination of a line through the points(5,14) and (9,18)

The inclination of the through the points (5, 14) and (9, 18) is 45°

Step-by-step explanation:

The given point has coordinates (5, 14) and (9, 18)

To find the inclination, θ, of the line passing the two points, with point 1 having coordinates (x₁, y₁) and point 2,  having coordinates (x₂, y₂), we have to look for the slope as follows;

The slope, m = Change in the y-coordinate ÷ Change in the x-coordinate

Where:

y₁ = The y-coordinate of point 1 = 14

x₁ = The x-coordinate of point 1 = 5

y₂ = The y-coordinate of point 2 = 18

x₂ = The x-coordinate of point 2 = 9

Substituting, we have;

The inclination of the line is the angle the line makes with x-axis

Since the slope gives the ratio of the opposite and adjacent segment to the angle of inclination, the arc-tangent of the slope will give the angle in degrees as follows;

given that m = 1, we have;

tan⁻¹(m) = θ = tan⁻¹(1) =  45°.

See below.

Step-by-step explanation:

No table is attached however. The answer here can be easily done. The inverse of a function is simply the (x,y) pairs of the function switched to (y,x). So in the table if the functions has (4,3) then the inverse is (3,4). So g(3) = 4. Find where the value of y in the table is 3 and the x value is g(3).