Find the slope of a line that is a) parallel and b) perpendicular to the given line.7x+5y=1

Answer:Parallel line should have slope = [tex]-\frac{7}{5}[/tex]Perpendicular line should have slope = [tex]\frac{5}{7}[/tex]Step-by-step explanation:First write this linear equation in slope y-intercept form in order to find what is its slope. This is done by simply solving for y in the given equation, and investigating which coefficient accompanies the term in "x" in that derived form:[tex]7x+5y=1\\5y=-7x+1\\y=-\frac{7}{5} x+\frac{1}{5}[/tex]therefore, the slope of this line is [tex]-\frac{7}{5}[/tex]Therefore, a line parallel to this one should have the same slope: [tex]\frac{7}{5}[/tex]On the other hand, for a line to be perpendicular to a given one, the perpendicular line must have a slope equal to the "opposite of the reciprocal" of the original line's slope. Where opposite means that it must have the opposite sign (so in our case it must be positive because our original line has a negative slope). And "reciprocal" means that we need to invert the fraction.Therefore a perpendicular line to the given one should have slope equals to: [tex]\frac{5}{7}[/tex]