Writing Linear Equations: 4.1-4.2 Review

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

To find the equation, identify the fixed cost and the variable cost per day. For example, if the company charges $75 for 3 days and $155 for 7 days, the equation is $$y = 20x + 15$$ , where $$x$$ is the number of days.

The equation $$y = -6$$ represents a horizontal line that crosses the y-axis at -6.

The standard form of a linear equation is written as $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers.

To convert $$y = mx + b$$ to standard form, rearrange it to the form $$Ax + By = C$$ .

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

The y-intercept is the value of $$b$$ in the equation $$y = mx + b$$ , which is the point where the line crosses the y-axis.

The slope indicates the steepness of the line and the direction of the relationship between $$x$$ and $$y$$ . A positive slope means the line rises, while a negative slope means it falls.

If the equation is of the form $$x = k$$ , it is vertical. If it is of the form $$y = k$$ , it is horizontal.

The equation of the line is $$4x - 3y = 3$$ .