Choose the equation of the line passing through the point (-1, 7) and perpendicular to y = -1/4 x - 5.

Question

I'm not understanding this at all!

Answer 1

There are two ways to fine the equation of a line.

 There is the slope-intercept equation or y- intercept form, which is y= mx +b.  m stands for the slope and b stands for the y-intercept, the place where the line crosses the y-axes.

The other equation is the point-slope form, y - y₁ = m ( x - x₁ ).

Y1 and x1 Is the coordinate of a known point.  m is the slope and x, y is any other point on the line.  Use this form when you  know one point on the line and the slope on the line.

You are given y = -(1/4)x - 5

Which form of the equation is this in?  The y-intercept form.  So m is -1/4.  That is the slope of the equation.  But you want a line that is perpendicular to that line.  Perpendicular lines cross each other at right angles.  The slope of the perpendicular line is the negative reciprical of the slope of the line.  To find the reciprocal, just flip over the fraction.  So the reciprocal of 2 is 1/2 and the reciprocal of 2/3 is 3/2.  So now you can find the slope of the equation you want to find.  The negative of a negative is a positive.  So the slope is 4.  Now you have the slope and a point so you are going to use the point slope form.

y - 7 = 4(x -(-1)).    

 y - 7 = 4(x + 1).  This is your answer.

 You can change this into the y-intercept form by distributing the 4.

y - 7 = 4x + 4.    Now bring the 7 to the other side by adding 7 to both sides.  

y = 4x + 11

Answer 2

Two lines are perpendicular if their slopes are opposite recipricals.  That means that the equation to compare the slopes is: m₁ = -1/m₂, where m₁ and m₂ are the slopes of the two lines.

The equation for the line that is perpendicular to the line we want is y =-1/4x -5, which means its slope is -1/4.

m₁ = -1/(-1/4)                 Equation for perpendicular slope with -1/4 substituted for m₂

m₁ = 4                            Simplified

Now that we have the slope of the line that we want (4) and a point (-1,7), we can use point-slope formula to find the equation of the line that we want.

y - y₁ = m(x - x₁)                       Point-slope formula

y - 7 = 4(x - (-1))                      Substitution

y - 7 = 4(x + 1)                         Subtracting a negative means adding a positive

y - 7 = 4x + 4                            Distributive property

y - 7 + 7 = 4x + 4 + 7                Add 7 to each side

y = 4x + 11                               Simplify