Questions: Find the equation of the line parallel to y=3x-7 that includes the point (-4, -6). Give your answer in Point-Slope Form. y-[?]=[?](x-[?]) Point-Slope Form: y-y1=m(x-x1)

Find the equation of the line parallel to y=3x-7 that includes the point (-4, -6).

Give your answer in Point-Slope Form.
y-[?]=[?](x-[?])

Point-Slope Form: y-y1=m(x-x1)

Transcript text: Find the equation of the line parallel to $y=3 x-7$ that includes the point (-4, -6). Give your answer in Point-Slope Form. \[ y-[?]=\square(x-\square) \] Point-Slope Form: $y-y_{1}=m\left(x-x_{1}\right)$

Solution

Solution Steps

To find the equation of a line parallel to a given line, we need to use the same slope as the given line. The slope of the line $ y = 3x - 7 $ is 3. Using the point-slope form of a line equation, we substitute the slope and the given point (-4, -6) into the formula $ y - y_1 = m(x - x_1) $.

Step 1: Identify the Slope

The slope of the given line $ y = 3x - 7 $ is $ m = 3 $. Since we are looking for a line that is parallel to this line, it will have the same slope.

Step 2: Use the Point-Slope Form

We will use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] Here, $ (x_1, y_1) = (-4, -6) $ is the point through which the line passes.

Step 3: Substitute Values into the Equation

Substituting the values into the point-slope form: \[ y - (-6) = 3(x - (-4)) \] This simplifies to: \[ y + 6 = 3(x + 4) \]