Questions: Write an equation for a line parallel to y=-3x+5 and passing through the point (2,-9) y=

Transcript text: Write an equation for a line parallel to $y=-3 x+5$ and passing through the point $(2,-9)$ \[ y= \] $\square$ Question Help: Video

Solution

Solution Steps

Step 1: Identify the slope of the given line

The equation of the given line is $ y = -3x + 5 $. The slope of this line is $ -3 $.

Step 2: Use the same slope for the parallel line

Since parallel lines have the same slope, the slope of the desired line is also $ -3 $.

Step 3: Use the point-slope form to find the equation

The point-slope form of a line is $ y - y_1 = m(x - x_1) $, where $ m $ is the slope and $ (x_1, y_1) $ is a point on the line. Substituting the slope $ m = -3 $ and the point $ (2, -9) $:

\[ y - (-9) = -3(x - 2) \]

Step 4: Simplify the equation

Simplify the equation to solve for $ y $:

\[ y + 9 = -3x + 6 \]

\[ y = -3x + 6 - 9 \]

\[ y = -3x - 3 \]

The equation of the line is:

\[ y = -3x - 3 \]

Final Answer

$\boxed{y = -3x - 3}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!