Questions: What is the point-slope form of a line with slope 4/5 that contains the point (-2,1) ? A. y+1=4/5(x+2) B. y+1=4/5(x-2) C. y-1=4/5(x-2) D. y-1=4/5(x+2)

Transcript text: What is the point-slope form of a line with slope $\frac{4}{5}$ that contains the point $(-2,1)$ ? A. $y+1=\frac{4}{5}(x+2)$ B. $y+1=\frac{4}{5}(x-2)$ C. $y-1=\frac{4}{5}(x-2)$ D. $y-1=\frac{4}{5}(x+2)$

Solution

Solution Steps

Step 1: Identify the given information

The slope of the line is $ \frac{4}{5} $, and it passes through the point $ (-2, 1) $.

Step 2: Recall the point-slope form

The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] where $ m $ is the slope, and $ (x_1, y_1) $ is a point on the line.

Step 3: Substitute the given values into the point-slope form

Substitute $ m = \frac{4}{5} $, $ x_1 = -2 $, and $ y_1 = 1 $ into the equation: \[ y - 1 = \frac{4}{5}(x - (-2)) \] Simplify the equation: \[ y - 1 = \frac{4}{5}(x + 2) \]

Final Answer

The correct answer is A: $ \boxed{y + 1 = \frac{4}{5}(x + 2)} $

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