Given: The equation below
[tex]5x+4y=6[/tex]To Determine: The slope of the line that is parallel to the graph of the given equation
Solution
Please note that two lines are parallel if their slopes are equal. Therefore, a line that is parallel to the given equation would have the same slope to the given
The slope can calculated as shown below
[tex]\begin{gathered} Slope-intercept\text{ form of a line is} \\ y=mx+c \\ m=slope \\ c=intercept\text{ on y-axis} \\ So, \\ 5x+4y=6 \\ 4y=6-5x \\ \frac{4y}{4}=\frac{6}{4}-\frac{5x}{4} \\ y=\frac{3}{2}-\frac{5}{4}x \\ y=-\frac{5}{4}x+\frac{3}{2} \\ Hence,slope\text{ is} \\ m=-\frac{5}{4} \end{gathered}[/tex]Hence, the slope of a line parallel to the graph of 5x + 4y = 6 is - 5/4
