What is an equation of the line that passes through the points left parenthesis, minus, 5, comma, 3, right parenthesis(−5,3) and left parenthesis, 5, comma, 5, right parenthesis(5,5)?

To find the equation of the line passing through the points \((-5, 3)\) and \( (5, 5) \), follow these steps:

### Step 1: Find the slope (m) of the line
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 of the points \((-5, 3)\) and \((5, 5)\):
\[
m = \frac{5 - 3}{5 - (-5)} = \frac{2}{10} = \frac{1}{5}
\]

### Step 2: Use the point-slope form to find the equation of the line
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-5, 3)\) and the slope \(m = \frac{1}{5}\), we get:
\[
y - 3 = \frac{1}{5}(x - (-5))
\]
Simplify:
\[
y - 3 = \frac{1}{5}(x + 5)
\]
Distribute the slope:
\[
y - 3 = \frac{1}{5}x + 1
\]
Add 3 to both sides:
\[
y = \frac{1}{5}x + 4
\]

### Final Equation of the Line:
\[
y = \frac{1}{5}x + 4
\]

Would you like a deeper explanation or more examples? Here are five related questions to explore further:

1. How do you derive the slope of a line from two points?
2. Can you convert the equation to standard form \(Ax + By = C\)?
3. What is the significance of the slope and intercept in a linear equation?
4. How would the equation change if the points were reversed?
5. How can you graph the line using the slope and intercept?

**Tip:** Always double-check your slope calculation to ensure accuracy when determining the equation of a line!

What is an equation of the line that passes through the points (−5,3) and (5,5)?

Learn how to find the equation of the line passing through the points (−5,3) and (5,5) using the slope formula and point-slope form. A detailed step-by-step solution, suitable for Grades 8-10, covering key algebraic concepts like slope and linear equations.

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