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Answer:
The linear function which represents the line given by the point-slope equation y – 2 = 4(x – 3) will be:
Hence, option D is correct.
Step-by-step explanation:
We know that the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
Given the equation
y – 2 = 4(x – 3)
comparing with the point-slope form of the line equation, we get
m = 4
(x₁, y₁) = (3, 2)
We also know the slope-intercept form of the line equation
y = mx + b
where m is the slope and b is the y-intercept
since we already fetched m = 4 and (x₁, y₁) = (3, 2)
so substitute m = 4 and (3, 2) in the slope-intercept form of the line equation to determine the y-intercept b
y = mx + b
2 = 4(3) + b
2 = 12 + b
flip the equation
12 + b = 2
subtract 12 from both sides
12 + b - 12 = 2 - 12
b = -10
now substitute b = -10 and m = 4 in the slope-intercept form of the line equation
y = mx + b
y = 4x + (-10)
y = 4x - 10
f(x) = 4x - 10 ∵ y = f(x)
Therefore, the linear function which represents the line given by the point-slope equation y – 2 = 4(x – 3) will be:
Hence, option D is correct.