Answer:
[tex]\frac{5}{3}[/tex]
Step-by-step explanation:
If the lines are perpendicular, then the slopes have the same absolute value, but opposite signs. So, to find the slope of the perpendicular, we first have to find the slope of line whose equation is 10x + 6y = -84. To do this, we'll convert the equation into slope-intercept form by isolating y:
10x + 6y = -84
6y = -84 - 10x
y = -84/6 - 10x/6
y = -14 - [tex]\frac{10}{6}[/tex]x
10/6 can be simplified to 5/3:
y = -[tex]\frac{5}{3}[/tex]x - 14
The slope of the first equations line is -5/3. So, the slope of the line perpendicular to this line is 5/3.
