Respuesta :
The line given is
[tex]7x-3y=10[/tex]The equation expressed in slope-intercept is now;
[tex]\begin{gathered} 7x-3y=10 \\ Subtract\text{ 7x from both sides of the equation;} \\ 7x-7x-3y=10-7x \\ -3y=10-7x \\ \text{Divide both sides by -3} \\ -\frac{3y}{-3}=\frac{10-7x}{-3} \\ y=-\frac{10}{3}-\frac{7}{-3}x \\ y=-\frac{10}{3}+\frac{7}{3}x \end{gathered}[/tex]Note that the slope of this line is the coefficient of x and that is
[tex]\frac{7}{3}[/tex]The slope of the line perpendicular to this one would be a negative inverse and that now gives us;
[tex]\begin{gathered} \text{Inverse}=\frac{3}{7} \\ \text{Negative inverse}=-\frac{3}{7} \end{gathered}[/tex]The slope of the line perpendicular is option C, (that is -3/7)
