Questions: Find an equation of the line L. L is parallel to y=-2x.

Transcript text: Find an equation of the line $L$. $L$ is parallel to $y=-2 x$.

Solution

Solution Steps

Step 1: Identify the Slope of the Given Line

The given line is $ y = -2x $. The slope ($ m $) of this line is $-2$.

Step 2: Formulate the Equation of the Parallel Line

A line parallel to the given line will have the same slope. Therefore, the equation of the line $ L $ will be: \[ y = -2x + b \] where $ b $ is the y-intercept, which can be any real number.

Step 3: Choose an Arbitrary Y-Intercept

For this example, we choose $ b = 3 $. Thus, the equation of the line $ L $ becomes: \[ y = -2x + 3 \]

Step 4: Calculate the Value of $ y $ for a Given $ x $

To find the value of $ y $ when $ x = 5 $, substitute $ x = 5 $ into the equation: \[ y = -2(5) + 3 \] \[ y = -10 + 3 \] \[ y = -7 \]

Final Answer

$\boxed{y = -2x + b}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >