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Answer:
The equation of the perpendicular line to y=-4*x-5 is [tex]y=\frac{1}{4}*x+\frac{7}{2}[/tex]
Step-by-step explanation:
Perpendicular lines are two or more lines that intersect at an angle of 90 degrees. Being y = m * x + b the equation of a line, two lines, with a slope other than zero, are orthogonal or perpenducillary if and only if the product of their slopes is -1. In other words, if two lines are perpendicular, they have their slopes reversed and sign changed.
In this case, with y = -4x-5 the slope will be -4. So the slope of the perpendicular line will be [tex]\frac{1}{4}[/tex]. Then the equation of the perpendicular line will be:
[tex]y=\frac{1}{4}* x+b[/tex]
To find the value of b, you know the value of the point (-2,3). So x = -2 and y = 3. Replacing in the equation of the perpendicular line, you have:
[tex]3=\frac{1}{4}* (-2)+b[/tex]
Solving, you get:
[tex]3=-\frac{1}{2}+b[/tex]
[tex]3+\frac{1}{2}=b[/tex]
[tex]\frac{7}{2}=b[/tex]
The equation of the perpendicular line to y=-4*x-5 is [tex]y=\frac{1}{4}*x+\frac{7}{2}[/tex]