Which is the equation of the line, in point-slope form, that has a slope of –4 and passes through the point (7, 1)?
(Points : 1)
y – 7 = 4(x – 1)
y – 1 = –4(x + 7)
y – 1 = –4(x – 7)
y – 7 = –4(x – 1)

Question

Which is the equation of the line, in point-slope form, that has a slope of –4 and passes through the point (7, 1)? 
(Points : 1)
       y – 7 = 4(x – 1)
       y – 1 = –4(x + 7)
       y – 1 = –4(x – 7)
       y – 7 = –4(x – 1)

anonymous · Answer

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                               Simplif

anonymous · Answer

*simplify