Find an equation of the line that contains the given pair of points.

​(17

​,

19

​),

​(5

​,

7

​)

To find the equation of the line passing through two points, we use the slope-intercept form of a line equation:

\[
y = mx + b
\]

Where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept.

### Step 1: Find the slope \( m \)

The formula to calculate the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the given points \((17, 19)\) and \((5, 7)\), we have:

\[
m = \frac{7 - 19}{5 - 17} = \frac{-12}{-12} = 1
\]

### Step 2: Use the point-slope form

Now that we know the slope \( m = 1 \), we can use the point-slope form of a line:

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

Using one of the points, say \((5, 7)\):

\[
y - 7 = 1(x - 5)
\]

### Step 3: Simplify the equation

\[
y - 7 = x - 5
\]

Add 7 to both sides:

\[
y = x + 2
\]

Thus, the equation of the line is:

\[
y = x + 2
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you find the equation of a line given its slope and y-intercept?
2. How can you verify if a point lies on a line?
3. What is the difference between the point-slope and slope-intercept forms of a line?
4. How do you determine the slope of a vertical line?
5. What is the general form of a linear equation?

**Tip:** Always recheck your slope calculations to avoid sign errors.

Find an equation of the line that contains the given pair of points (17, 19), (5, 7)

Learn how to find the equation of a line passing through the points (17, 19) and (5, 7). This problem covers key algebraic concepts like the slope formula, point-slope form, and slope-intercept form. Ideal for students in Grades 7-10.

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