Question

2,2 6,4
what is the initial value of the function
rate of change: 1/2

Answer 1

To find the initial value of a function given a point and a rate of change (slope), we can use the slope-intercept form of a linear equation, which is:

\[ y = mx + b \]

Where:
- \( m \) is the slope (rate of change)
- \( b \) is the y-intercept (initial value)
- \( (x, y) \) is a point on the line

In this case, you've provided the point (2,2) and a rate of change (slope) as \( \frac{1}{2} \).

We can plug the point and the slope into the equation to solve for \( b \):

1. Start with the point (2,2):
\[ 2 = \frac{1}{2}(2) + b \]

2. Calculate \( \frac{1}{2}(2) \):
\[ 2 = 1 + b \]

3. Subtract 1 from both sides to find \( b \):
\[ b = 2 - 1 \]
\[ b = 1 \]

Therefore, the initial value of the function (y-intercept) is \( 1 \).

So the equation of the function is:
\[ y = \frac{1}{2}x + 1 \]