Questions: Write the equation of the line that passes through the points (-7,0) and (-3,-4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Write the equation of the line that passes through the points (-7,0) and (-3,-4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Transcript text: Write the equation of the line that passes through the points $(-7,0)$ and $(-3,-4)$. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Solution

Solution Steps

To find the equation of the line passing through two points, we first calculate the slope using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Then, we use the point-slope form of the equation of a line, which is $ y - y_1 = m(x - x_1) $, using one of the given points.

Step 1: Calculate the Slope

To find the slope $ m $ of the line passing through the points $(-7, 0)$ and $(-3, -4)$, we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 0}{-3 - (-7)} = \frac{-4}{4} = -1.0 \]

Step 2: Use Point-Slope Form

Now that we have the slope $ m = -1.0 $, we can use the point-slope form of the equation of a line, which is given by:

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

Substituting $ m = -1.0 $, $ x_1 = -7 $, and $ y_1 = 0 $:

\[ y - 0 = -1.0(x - (-7)) \]

This simplifies to:

\[ y = -1.0(x + 7) \]

Step 3: Simplify the Equation

Distributing the slope: