Respuesta :
The general slope intercept form equation of a line is as stated below;
[tex]y=mx+b[/tex]where m is the slope and b is the intercept.
If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.
The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;
So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);
Remember, the point slope form equation of a line is given as;
[tex]y-y_1=m(x-x_{1)}[/tex]Substituting the above values, we'll have
[tex]y-7=-\frac{1}{5}(x+5)[/tex]Let's open up the parenthesis first, we'll have;
[tex]\begin{gathered} y-7=-\frac{1}{5}x-\frac{5}{5} \\ y-7=-\frac{1}{5}x-1 \end{gathered}[/tex]Let's isolate y by adding 7 to both sides of the equation;
[tex]y=-\frac{1}{5}x+6[/tex]The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).
