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

To find the equation of the line passing through the points \((-7, 0)\) and \((-3, -4)\), follow these steps:

1. **Calculate the slope** (\(m\)) of the line using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   where \((x_1, y_1) = (-7, 0)\) and \((x_2, y_2) = (-3, -4)\).

   \[
   m = \frac{-4 - 0}{-3 - (-7)} = \frac{-4}{-3 + 7} = \frac{-4}{4} = -1
   \]

2. **Use the point-slope form** of the equation of a line, which is:
   \[
   y - y_1 = m(x - x_1)
   \]

   Substitute the slope \(m = -1\) and one of the points, say \((-7, 0)\):

   \[
   y - 0 = -1(x - (-7))
   \]

3. **Simplify the equation**:
   \[
   y = -1(x + 7)
   \]

   \[
   y = -x - 7
   \]

So, the equation of the line in point-slope form is:
\[
y = -x - 7
\]

Would you like further details or have any questions?

Here are some related questions you might find helpful:

1. How do you convert this equation to standard form?
2. What is the y-intercept of this line?
3. How would you graph this line?
4. What is the equation of a line parallel to this one that passes through a different point?
5. How would the equation change if the slope were positive instead of negative?

**Tip:** Always remember to simplify the slope as much as possible before using it in the point-slope form.

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.

Learn how to find the equation of the line that passes through the points (-7, 0) and (-3, -4) using the point-slope form. This step-by-step guide covers algebraic concepts such as the slope formula and point-slope form, making it ideal for students in Grades 8-10.

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