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Write a function in the form y = mx + b for the line that contains the points (–8.3, –5.2) and (6.4, 9.5).
The data in the table below represent a linear relationship. Fill in the missing data.
x 10 20 30 40
? ? ? ?
To find the equation of the line in the form ( y = mx + b ) that passes through the points ( (-8.3, -5.2) ) and ( (6.4, 9.5) ), we need to follow these steps:
1. Calculate the slope (m):
The formula for 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}
]
Substituting the given points:
[
m = frac{9.5 – (-5.2)}{6.4 – (-8.3)} = frac{9.5 + 5.2}{6.4 + 8.3} = frac{14.7}{14.7} = 1
]
2. Use one of the points to find the y-intercept (b):
We can use the point ( (6.4, 9.5) ) to find ( b ):
[
y = mx + b Rightarrow 9.5 = 1(6.4) + b
]
[
9.5 = 6.4 + b