In this item, we may generate the coordinates of the point to which the points of the given function lie.
For F(-4) = -5, the value of x = -4 and y = -5. Therefore, the coordinates of the point are (-4, -5)
For F(1) = 4, the value of x = 1 and y = 4. Hence, the coordinates of the point are (1, 4)
To generate the linear equation, we use the two-point formula:
(y - y₁) = ((y₂ - y₁)/(x₂ - x₁))(x - x₁)
Substituting the known values,
y - (-5) = ((4 - (-5)) / (1 - (-4))( x - (-4))
Simplifying,
y + 5 = 9x/5 + 36/5
Multiplying the equation by 5,
5y = 9x + 11
In standard form,
9x - 5y = -11