Generate the equation of a line given its graph

The slope-intercept form is given by the equation $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

The slope is determined by the rise over run, calculated as the change in y divided by the change in x between two points on the line.

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

The y-intercept is the point where the line crosses the y-axis, represented by the value of $$b$$ in the slope-intercept form $$y = mx + b$$ .

To find the equation, first calculate the slope $$m$$ using the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ , then use one of the points to solve for $$b$$ in the slope-intercept form.

The equation of a vertical line is of the form $$x = a$$ , where $$a$$ is the x-coordinate of any point on the line.

The equation of a horizontal line is of the form $$y = b$$ , where $$b$$ is the y-coordinate of any point on the line.

To graph this equation, start at the y-intercept (0,3) and use the slope (2) to rise 2 units up and run 1 unit to the right.

The slope represents the rate of change, such as speed in a distance-time graph or cost per item in a price-quantity graph.