To find the equation of the tangent line to the graph of the function at the given point, we first need to clarify the function. If we assume the function is given incorrectly and is actually written as y = 4x + 6, then we can proceed. The point given appears to be (x,y) = (5,32).
1. **Find the derivative of the function**:
The derivative of the function, which represents the slope of the tangent line, needs to be calculated. For the function
y = 4x + 6, the derivative is:
dy/dx = 4.
2. **Use the point-slope form of the equation**:
The point-slope form of a line is given by:
y – y₁ = m(x – x₁),
where m is the slope and (x₁, y₁) is the given point. Substituting the values:
– m = 4
– (x₁, y₁) = (5, 32)
y – 32 = 4(x – 5)
3. **Simplify the equation**:
Expanding the equation gives us:
y – 32 = 4x – 20,
which simplifies to:
y = 4x + 12.
So, the equation of the tangent line at the point (5, 32) is y = 4x + 12.