Questions: Find the equation of the line: Point ( 0,5 ); Slope = -2

Find the equation of the line: Point ( 0,5 ); Slope = -2
Transcript text: Find the equation of the line: Point ( 0,5 ); Slope $=-2$
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Solution

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Solution Steps

To find the equation of a line given a point and a slope, we can use the point-slope form of a linear equation, which is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the given point. Substitute the given point and slope into this formula to find the equation of the line.

Step 1: Identify the Given Information

We are given a point \( (0, 5) \) and a slope \( m = -2 \).

Step 2: Use the Point-Slope Form

We will use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] Substituting the values \( (x_1, y_1) = (0, 5) \) and \( m = -2 \) into the equation, we have: \[ y - 5 = -2(x - 0) \]

Step 3: Simplify the Equation

Now, we simplify the equation: \[ y - 5 = -2x \] Adding \( 5 \) to both sides gives: \[ y = -2x + 5 \]

Final Answer

The equation of the line is \[ \boxed{y = -2x + 5} \]

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