Write the slope intercept form of the equation of the line through the given points (-1,-1) and (-5,-5)

To find the equation of a line in slope-intercept form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

### Step 1: Calculate the slope
The slope \( m \) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points \((-1, -1)\) and \((-5, -5)\), let \((x_1, y_1) = (-1, -1)\) and \((x_2, y_2) = (-5, -5)\).

Now, calculate the slope:
\[
m = \frac{-5 - (-1)}{-5 - (-1)} = \frac{-5 + 1}{-5 + 1} = \frac{-4}{-4} = 1
\]

### Step 2: Use point-slope form
We now use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
Substitute \(m = 1\), \(x_1 = -1\), and \(y_1 = -1\):
\[
y - (-1) = 1(x - (-1))
\]
Simplifying this equation:
\[
y + 1 = x + 1
\]
Subtract 1 from both sides:
\[
y = x
\]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = x
\]

Would you like more details on this, or do you have any questions?

Here are 5 related questions to explore further:
1. How do you find the slope of a line parallel to a given line?
2. What is the slope of a vertical line?
3. How can you find the y-intercept if you're given the slope and one point?
4. How do you find the equation of a line perpendicular to another line?
5. How does the slope-intercept form relate to the standard form of a line equation?

**Tip:** Always double-check your slope calculations to avoid sign errors when subtracting coordinates.

Learn how to find the slope-intercept form of a line passing through the points (-1, -1) and (-5, -5). This step-by-step solution covers key algebraic concepts such as slope calculation and converting to the slope-intercept form. Suitable for students in Grades 7-9.

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