In coordinate geometry, we often encounter the need to write equations of lines. There are different forms to represent a line's equation, such as slope-intercept form (y = mx + b) and point-slope form (y - y1 = m(x - x1)). Let's explore these forms and understand how to use them:

Slope-Intercept Form: This form is written as y = mx + b. Here, 'm' represents the slope of the line, and 'b' represents the y-intercept, which is the point where the line crosses the y-axis. To write the equation of a line in slope-intercept form, you need to know its slope and the y-intercept.

For example, let’s say we have a line with a slope of 2 and a y-intercept of 3. The equation of this line would be y = 2x + 3.

Point-Slope Form: In this form, we use a specific point on the line (x1, y1) and the slope 'm' to write the equation. The point-slope form is given by y - y1 = m(x - x1).

For instance, if we have a line with a slope of 3 passing through the point (2, 4), the equation in point-slope form would be y - 4 = 3(x - 2).

Remember, different forms of the equation of a line provide different information and may be useful in different situations. Practice using both forms to become comfortable with writing equations of lines.