Question

If a function has rate of change one half
and yequals11 when xequals2​, write its equation.

Answer 1

To find the equation of a linear function based on the information provided, we can use the point-slope form of a linear equation, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \(m\) is the rate of change (slope), and \((x_1, y_1)\) is a point on the line.

Given:
- Rate of change (slope) \(m = \frac{1}{2}\)
- Point \((x_1, y_1) = (2, 11)\)

We can substitute these values into the point-slope form:

\[
y - 11 = \frac{1}{2}(x - 2)
\]

Now, we simplify this equation:

\[
y - 11 = \frac{1}{2}x - 1
\]

Now, adding 11 to both sides:

\[
y = \frac{1}{2}x - 1 + 11
\]

\[
y = \frac{1}{2}x + 10
\]

Thus, the equation of the function is:

\[
y = \frac{1}{2}x + 10
\]