Writing Equation of a Line from a Graph

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

The slope can be identified by calculating the rise over run between two points on the line. It is the change in y divided by the change in x.

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

If the slope $$m$$ is positive, the line is increasing. If the slope $$m$$ is negative, the line is decreasing.

The equation is $$y = 2x - 1$$ .

To convert to standard form, rearrange the equation to the form $$Ax + By = C$$ , where A, B, and C are integers.

The slope of the line is $$-\frac{3}{4}$$ .

First, find the slope: $$m = \frac{6-2}{3-1} = 2$$ . Then use point-slope form: $$y - 2 = 2(x - 1)$$ , which simplifies to $$y = 2x$$ .

Two lines are parallel if they have the same slope but different y-intercepts.

The equation of a horizontal line is of the form $$y = b$$ , where $$b$$ is a constant.