What is the equation of the line that passes through the point left parenthesis, minus, 2, comma, minus, 8, right parenthesis(−2,−8) and has a slope of 1?


To find the equation of a line that passes through the point \((-2, -8)\) and has a slope of \(m = 1\), we use the point-slope form of the equation of a line, which is:

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

where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line.

### Step 1: Substitute the given values
Here, \(m = 1\), \(x_1 = -2\), and \(y_1 = -8\). Substituting these into the point-slope form gives:

\[
y - (-8) = 1(x - (-2))
\]

which simplifies to:

\[
y + 8 = 1(x + 2)
\]

### Step 2: Simplify the equation
Expanding the right-hand side:

\[
y + 8 = x + 2
\]

Subtract 8 from both sides to solve for \(y\):

\[
y = x - 6
\]

Thus, the equation of the line is:

\[
y = x - 6
\]

Would you like more details or have any questions about this process?

Here are 5 related questions to deepen your understanding:
1. How do you convert from point-slope form to slope-intercept form?
2. What is the equation of a line with a slope of 2 passing through the point (3, 4)?
3. How do you find the slope of a line given two points?
4. How would the equation change if the slope were \(-1\) instead of \(1\)?
5. What is the significance of the slope in the equation of a line?

**Tip:** The slope-intercept form of a line equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

What is the equation of the line that passes through the point (−2,−8) and has a slope of 1?

Learn how to find the equation of a line that passes through the point (−2,−8) with a slope of 1. This solution explains the point-slope and slope-intercept forms and provides a step-by-step breakdown for students in Grades 8-10.

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