Point (5,3) lies on curve y=sqrt(x+4).
If Q is the point (x,sqrt(x+4)), use your calculator to find the slope of the secant line PQ for the following values of x.
a)x=4.5
I just want help on this one. What do I do?
I don't even understand the question.
You have the point 5,3
figure y for the x=4.5
so you have two points. Now figure the secant slope between those points.
To find the slope of the secant line PQ for the given value of x, we need to determine the coordinates of points P and Q, and then calculate the slope using the formula:
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
First, let's find the coordinates of point Q:
Q has the coordinates (x, sqrt(x+4)), where x = 4.5 (as given in the question). So, substituting x into the equation:
Q = (4.5, sqrt(4.5+4))
Next, we need to find the coordinates of point P:
P has the coordinates (x₁, y₁), where x₁ = 5 and y₁ = 3 (as given in the question).
Now, we can calculate the slope of the secant line PQ using the formula mentioned earlier:
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
Substituting the known coordinates of P and Q:
Slope (m) = (sqrt(4.5+4) - 3) / (4.5 - 5)
You can input this expression into a calculator to find the value of the slope.