To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points (0, 2.3) and (5, -1.9), we need to calculate the slope (m) first.
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Calculate the slope (m): The formula to calculate the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0, 2.3) and (5, -1.9):
- \( x_1 = 0 \), \( y_1 = 2.3 \)
- \( x_2 = 5 \), \( y_2 = -1.9 \)
Plugging in the values: \[ m = \frac{-1.9 - 2.3}{5 - 0} = \frac{-4.2}{5} = -0.84 \]
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Use the slope and a point to find the y-intercept (b): We can use the point (0, 2.3) to find \( b \). The coordinate point tells us that when \( x = 0 \), \( y = 2.3 \), which is also the y-intercept.
Therefore, \( b = 2.3 \).
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Write the equation in slope-intercept form: Now that we have \( m \) and \( b \), we can write the equation: \[ y = -0.84x + 2.3 \]
So, the equation in slope-intercept form is: \[ y = -0.84x + 2.3 \]
To fill in your blanks:
blank equals blank x + blank would be:
- y equals -0.84 x + 2.3.
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