Questions: Find an equation of the line L. L is parallel to y=3x. The equation is □ (Type an equation. Simplify your answer.)

Transcript text: Find an equation of the line $L$. $L$ is parallel to $y=3 x$. The equation is $\square$ (Type an equation. Simplify your answer.)

Solution

Solution Steps

Step 1: Identify the slope of the given line

The given line is $ y = 3x $. The slope of this line is 3.

Step 2: Use the point-slope form of the equation

Since line $ L $ is parallel to $ y = 3x $, it has the same slope, which is 3. The point given on line $ L $ is (2, 1). We use the point-slope form of the equation: \[ y - y_1 = m(x - x_1) \] where $ m $ is the slope and $ (x_1, y_1) $ is the point.

Step 3: Substitute the slope and point into the point-slope form

Substitute $ m = 3 $, $ x_1 = 2 $, and $ y_1 = 1 $ into the equation: \[ y - 1 = 3(x - 2) \]

Step 4: Simplify the equation

Distribute and simplify the equation: \[ y - 1 = 3x - 6 \] \[ y = 3x - 5 \]

Final Answer

The equation of the line $ L $ is: \[ y = 3x - 5 \]

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