To find the equation of the line in slope-intercept form \( y = mx + b \), we need to calculate the slope \( m \) using the two given points \((-4, -5)\) and \( (4, 5)\).
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Calculate the slope (m): The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the values:
- \( (x_1, y_1) = (-4, -5) \)
- \( (x_2, y_2) = (4, 5) \)
\[ m = \frac{5 - (-5)}{4 - (-4)} = \frac{5 + 5}{4 + 4} = \frac{10}{8} = \frac{5}{4} \]
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Use the slope and a point to find the y-intercept (b): We can use one of the points to find the y-intercept. Let's use the point \((4, 5)\): \[ y = mx + b \] Plugging in the slope and the coordinates of the point: \[ 5 = \frac{5}{4}(4) + b \] \[ 5 = 5 + b \] \[ b = 5 - 5 = 0 \]
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Write the equation in slope-intercept form: Now we can write the equation of the line: \[ y = \frac{5}{4}x + 0 \] or simply: \[ y = \frac{5}{4}x \]
Thus, the equation of the line in slope-intercept form is \( y = \frac{5}{4}x \).