Write the equation of the line that passes through the points left parenthesis, 2, comma, minus, 8, right parenthesis(2,−8) and left parenthesis, 6, comma, minus, 7, right parenthesis(6,−7). 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 \((2, -8)\) and \((6, -7)\), we need to follow these steps:

### Step 1: Calculate the slope (m)
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the coordinates \((x_1, y_1) = (2, -8)\) and \((x_2, y_2) = (6, -7)\) into the slope formula:

\[
m = \frac{-7 - (-8)}{6 - 2} = \frac{-7 + 8}{4} = \frac{1}{4}
\]

### Step 2: Use the point-slope form
The point-slope form of a line is:

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

We can use either of the given points; let’s use the point \((2, -8)\). Substituting \(m = \frac{1}{4}\), \(x_1 = 2\), and \(y_1 = -8\) into the formula:

\[
y - (-8) = \frac{1}{4}(x - 2)
\]

Simplifying:

\[
y + 8 = \frac{1}{4}(x - 2)
\]

This is the equation of the line in simplified point-slope form.

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. How do you convert point-slope form to slope-intercept form?
2. How would the equation change if we used the other point \((6, -7)\)?
3. What is the y-intercept of this line?
4. How can we find the equation if the points form a vertical line?
5. What is the significance of the slope value being positive or negative?

**Tip:** In point-slope form, using any point on the line will give you the same equation.

Write the equation of the line that passes through the points (2,−8) and (6,−7). 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 passing through the points (2,−8) and (6,−7) using the point-slope formula. This detailed solution explains how to calculate the slope and apply the point-slope form for a clear, step-by-step result. Suitable for students in Grades 8-10.

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