Writing Equation of a Line from a 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 calculated as the rise over run, which is the change in y divided by the change in x between two points on the line.

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

A slope of 2 means that for every 1 unit increase in x, the value of y increases by 2 units.

The equation is $$y = -1x + 4$$ or simply $$y = -x + 4$$ .

First, calculate the slope using the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ . Then, use one of the points and the slope to write the equation in slope-intercept form.

A positive slope indicates that the line rises as it moves from left to right on the graph.

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

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

You can identify the slope by selecting two points on the line, calculating the rise (change in y) and run (change in x), and then using the formula $$m = \frac{rise}{run}$$ .