Welcome to our lesson on writing equations in slope-intercept form given two points!

To start, we'll determine the slope using the slope formula. Finding the slope is crucial as it represents the rate at which the line is rising or falling.

Next, we'll solve for the y-intercept, which is the point where the line intersects the y-axis. This can be found by substituting the slope and one of the points into the slope-intercept form equation y = mx + b, where b represents the y-intercept.

Finally, combining the slope and the y-intercept, we can write the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

This form makes it easy to identify the slope and y-intercept at a glance, making it a powerful tool in graphing linear equations. Let's dive into some examples to solidify these concepts!