To derive the equation of a line in slope-intercept form, we use the formula:
\[ y = mx + b \]
where \( m \) is the slope of the line and \( b \) is the y-intercept.
Step 1: Calculate the Slope (m)
The slope \( m \) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Given the points (0, 4) and (1, 8):
- Point 1: \( (x_1, y_1) = (0, 4) \)
- Point 2: \( (x_2, y_2) = (1, 8) \)
Substituting these values into the slope formula:
\[ m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4 \]
Step 2: Find the y-intercept (b)
To find the y-intercept \( b \), we can use one of the points and the slope. We'll use the point \( (0, 4) \). The y-intercept is the \( y \)-coordinate when \( x = 0 \). From the point, we can see:
\[ b = 4 \]
Step 3: Write the Equation in Slope-Intercept Form
Now we can write the equation of the line using the slope and y-intercept we found:
\[ y = 4x + 4 \]
Final Result
Thus, the equation of the line in slope-intercept form is:
\[ y = 4x + 4 \]
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