To find the equation of the line described by the points (1, 8) and (4, 17), you can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Step 1: Calculate the slope (m)
The slope \( m \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (1, 8) and (4, 17):
- \( (x_1, y_1) = (1, 8) \)
- \( (x_2, y_2) = (4, 17) \)
\[ m = \frac{17 - 8}{4 - 1} = \frac{9}{3} = 3 \]
Step 2: Use the slope to find the y-intercept (b)
Now that we have the slope \( m = 3 \), we can use one of the points to find \( b \). We'll use the point (1, 8):
\[ y = mx + b \] \[ 8 = 3(1) + b \] \[ 8 = 3 + b \] \[ b = 8 - 3 = 5 \]
Step 3: Write the equation
Now we have both components for the equation:
\[ y = 3x + 5 \]
So the completed equation is:
\[ y = 3x + 5 \]
Thus, the values to complete the equation \( y = \text{blank} \times x + \text{blank} \) are:
- Slope (m): 3
- Y-intercept (b): 5
So, the final answer would be \( y = 3x + 5 \).
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