Introduction:

Determining the equation of a line from two points on the line is a fundamental concept in algebra and geometry. This process involves using the coordinates of the two points to find the slope and then the equation of the line.



Understanding the Process:



The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Steps for Finding the Equation:



Calculate the slope (m) using the coordinates of the two points.

Use one of the points and the slope to find the y-intercept (b).

Substitute m and b into the slope-intercept form to get the equation of the line.

Example:



Given two points (2, 3) and (4, 7):

First, calculate the slope: m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Choose one point, say (2, 3), and use it with the slope to find b:

3 = 2(2) + b, solving for b gives b = -1.

The equation of the line is y = 2x - 1.

Key Points to Remember:



The slope is a measure of how steep the line is.

The y-intercept is where the line crosses the y-axis.