We want to find the equation of the tangent line to a given point in a given function.
The correct option is B: 13*x + y = 18
So we want to find the equation of the tangent line to the function.
[tex]y = \frac{2x + 3}{3x - 2}[/tex]
at the point (1, 5).
To get the slope of that line, we need to evaluate the derivate of the function in the x-value of the point, the derivate of the function will be:
[tex]y' = \frac{2}{3x - 2} - 3*\frac{2x + 3}{(3x - 2)^2}[/tex]
Now we evaluate this in the x-value of the point, which is x = 1.
[tex]y' = \frac{2}{3*1 - 2} - 3*\frac{2*1 + 3}{(3*1 - 2)^2} = -13[/tex]
Then the line will be something like:
y = -13*x + b
To find the value of b, we use the fact that the line must pass through the point (1, 5). This means that when x = 1, we have y = 5.
Replacing that in the line equation we get:
5 = -13*1 + b
5 + 13 = b
18 = b
Then the equation of the line is:
y = -13*x + 18
Or, rewriting it.
13*x + y = 18
So the correct option is B.
If you want to learn more, you can read:
https://brainly.com/question/23265136
