To find the equation of a line given two points, you follow these steps:

1. Use the two points to find the slope (m):

If the points are $(x_1, y_1)$ and $(x_2, y_2)$, the slope of the line is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

2. Use the point-slope form of the equation:

The equation of a line can be written in point-slope form:

$y - y_1 = m(x - x_1)$

Here, $m$ is the slope (calculated in Step 1) and $(x_1, y_1)$ is one of the given points.

3. Simplify to the slope-intercept form (if needed):

To express the equation in slope-intercept form ($y = mx + b$), solve for $y$ and simplify. If necessary, substitute one of the points into the equation to find the y-intercept ($b$).

---

Example:

Find the equation of the line passing through the points $(2, 3)$ and $(4, 7)$.

1. Calculate the slope: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2$

2. Write the point-slope form: Using point $(2, 3)$, $y - 3 = 2(x - 2)$

3. Simplify to slope-intercept form: Expand and simplify: $y - 3 = 2x - 4 \implies y = 2x - 1$

Thus, the equation of the line is: $y = 2x - 1$

---

Do you want me to demonstrate with a specific example or clarify any step?

Related Questions:

1. How do you find the equation of a vertical line given two points?
2. What is the general form of a linear equation, and how does it relate to point-slope form?
3. How can you verify that a point lies on a given line?
4. What is the equation of a line parallel to another line passing through a specific point?
5. How do you find the midpoint of the line segment between two points?

Tip:

Always check the coordinates carefully when calculating the slope to avoid sign errors!