Which equation is the equation of a line that passes through (-10. 3) and is perpendicular to #y=5x-7#?

1 Answer
Jan 8, 2017

Answer:

#y=-1/5 x +1#

Explanation:

I assume there is a typo and the problem should be:

write the equation of a line that passes through #(-10,3)# and is perpendicular to #y=5x-7#.

The line #y=5x-7# is in slope-intercept form #y=mx+b# where #m# is the slope. The slope of this line is thus #m=5#.

Perpendicular lines have slopes which are negative reciprocals. In other words, take the reciprocal of the slope and change the sign.

The negative reciprocal of #5# is #-1/5#.

To find the equation of a line which passes through #(color(red)(-10),color(red)3)# and with a slope of #color(blue)m= color(blue)(-1/5)#, use the point- slope formula:

#y-color(red)(y_1)=color(blue)m(x-color(red)(x_1))# where #(color(red)(x_1),color(red)( y_1))# is a point and #color(blue)m# is the slope.

#y-color(red)(3)=color(blue)(-1/5)(x-color(red)(-10))#

#y-3=-1/5(x+10)color(white)(aaa)# Equation in point-slope form

To put the equation in slope-intercept form, distribute the #-1/5#.

#y-3=-1/5 x-2#

Add 3 to both sides.

#y-3=-1/5 x-2#
#color(white)a+3color(white)(aaaaaaaa)+3#

#y=-1/5 x +1#