To find the rate of change (slope) and the initial value (y-intercept) for the given points, you need to determine the equation of the line that passes through these points.
Given points are:
- \( (2, 22) \)
- \( (8, 25) \)
### Step 1: Calculate the Rate of Change (Slope)
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substitute the given points:
\[ m = \frac{25 - 22}{8 - 2} = \frac{3}{6} = \frac{1}{2} \]
So, the rate of change (slope) is \( \frac{1}{2} \).
### Step 2: Find the Initial Value (Y-intercept)
The equation of a line in slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Using one of the points, say \((2, 22)\), you can substitute \( x = 2 \), \( y = 22 \), and \( m = \frac{1}{2} \) into the equation to solve for \( b \):
\[ 22 = \frac{1}{2} \cdot 2 + b \]
\[ 22 = 1 + b \]
\[ b = 22 - 1 \]
\[ b = 21 \]
So, the initial value (y-intercept) is \( 21 \).
### Conclusion
- The rate of change (slope) \( m \) is \( \frac{1}{2} \)
- The initial value (y-intercept) \( b \) is \( 21 \)
The equation of the line is:
\[ y = \frac{1}{2}x + 21 \]
C is 2 and 8 y is 22 and 25 what’s the rate of change and the initial value
1 answer
1 answer