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.