To find the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) using the two points provided: (-6, -6) and (2, 5).
The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let:
- \( (x_1, y_1) = (-6, -6) \)
- \( (x_2, y_2) = (2, 5) \)
Substituting the points into the slope formula gives: \[ m = \frac{5 - (-6)}{2 - (-6)} = \frac{5 + 6}{2 + 6} = \frac{11}{8} \]
Now that we have the slope \( m = \frac{11}{8} \), we can use one of the points to find the y-intercept (b). We'll use the point (2, 5).
The slope-intercept form is: \[ y = mx + b \]
Substituting the known values: \[ 5 = \frac{11}{8}(2) + b \] \[ 5 = \frac{22}{8} + b \] \[ 5 = \frac{11}{4} + b \]
To isolate \( b \), we can subtract \( \frac{11}{4} \) from both sides. First, convert 5 to a fraction with a denominator of 4: \[ 5 = \frac{20}{4} \] Now rearranging gives: \[ \frac{20}{4} - \frac{11}{4} = b \] \[ b = \frac{9}{4} \]
Now we have the slope and the y-intercept. The equation of the line in slope-intercept form is: \[ y = \frac{11}{8}x + \frac{9}{4} \]
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