Questions: What is the equation of the line L that passes through the point (-2,2) and has slope 2 ? Select one: a. y=2 x+5 b. y=2 x-5 c. y=1/2 x-2 d. y=2 x+6

What is the equation of the line L that passes through the point (-2,2) and has slope 2 ? Select one: a. y=2 x+5 b. y=2 x-5 c. y=1/2 x-2 d. y=2 x+6
Transcript text: What is the equation of the line $L$ that passes through the point $(-2,2)$ and has slope 2 ? Select one: a. $y=2 x+5$ b. $y=2 x-5$ c. $y=\frac{1}{2} x-2$ d. $y=2 x+6$
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Solution

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Solution Steps

Step 1: Identify the Point-Slope Form

The point-slope form of a line is given by the equation:

\[ y - y_1 = m(x - x_1) \]

where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

Step 2: Substitute the Given Values

We are given the point \((-2, 2)\) and the slope \(m = 2\). Substituting these values into the point-slope form, we have:

\[ y - 2 = 2(x + 2) \]

Step 3: Simplify the Equation

Distribute the slope on the right side:

\[ y - 2 = 2x + 4 \]

Add 2 to both sides to solve for \(y\):

\[ y = 2x + 6 \]

Final Answer

The equation of the line is \(\boxed{y = 2x + 6}\).

The correct choice is d. \( y = 2x + 6 \).

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