4.2 Writing Equations (Given 2 points)

To write an equation in slope-intercept form (y = mx + b), follow these steps:

1. Identify the slope (m) of the line. The slope is the change in y divided by the change in x between any two points on the line.

2. Identify the y-intercept (b) of the line. The y-intercept is the point where the line intersects the y-axis, and it has an x-coordinate of 0.

3. Write the equation in slope-intercept form using the slope and y-intercept.

For example, suppose you are given the line that passes through the points (2, 5) and (4, 9). To write the equation in slope-intercept form, follow these steps:

1. Find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates (2, 5) and (4, 9), we get:

m = (9 - 5) / (4 - 2) = 2

1. Find the y-intercept of the line by plugging in the coordinates (0, b) and solving for b using the slope-intercept form. Since the line passes through (2, 5), we can write:

5 = 2(2) + b

Solving for b, we get:

b = 1

1. Write the equation in slope-intercept form using the slope and y-intercept:

y = 2x + 1

So the equation of the line passing through the points (2, 5) and (4, 9) in slope-intercept form is y = 2x + 1.