Write a linear function that satisfies the given condition
F(0)=12, f(3)=-2
To write the linear function that satisfies the given condition, let's start by finding the slope (m) of the line using the two given points: F(0) = 12 and F(3) = -2.
The slope formula (m) is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the given points, we can substitute the values into the formula.
m = (-2 - 12) / (3 - 0)
m = -14 / 3
Now that we have the slope, we can use the point-slope form of a linear equation to write the function. The point-slope form is:
y - y1 = m(x - x1)
Using one of the given points, F(0) = 12, we can substitute the values to get the equation:
y - 12 = (-14 / 3)(x - 0)
Simplifying the equation further, we have:
y - 12 = (-14 / 3)x
To put it in standard form, we can distribute the (-14 / 3) term:
y - 12 = (-14 / 3)x -> y = (-14 / 3)x + 12
Therefore, the linear function that satisfies the given condition is:
F(x) = (-14 / 3)x + 12
since the slope is -14/3,
y = -14/3 x + 12