Bachman Matching an Equation of a Line with 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.

In the slope-intercept form $$y = mx + b$$ , the slope is represented by the coefficient $$m$$ .

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

To convert from standard form $$Ax + By = C$$ to slope-intercept form, solve for $$y$$ : $$y = -\frac{A}{B}x + \frac{C}{B}$$ .

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 slope of the line is 3, which means for every unit increase in $$x$$ , $$y$$ increases by 3.

The y-intercept is 5, which means the line crosses the y-axis at the point (0, 5).

The slope of the line is $$-\frac{1}{2}$$ , indicating that for every 2 units increase in $$x$$ , $$y$$ decreases by 1.

Two lines are parallel if they have the same slope. In slope-intercept form, this means they have the same value of $$m$$ .