What is the equation of the line perpendicular to #y=-15/7x # that passes through # (-1,7) #?

1 Answer
Jul 1, 2018

Answer:

Point-slope form: #y-7=7/15(x+1)#

Slope-intercept form: #y=7/15x+112/15#

Explanation:

The slope of a perpendicular line is the negative reciprocal of the original slope. In this case, the perpendicular slope of #-15/7# is #7/15#. The product of two perpendicular slopes is #-1#.

#-15/7xx7/15=-1#

With the slope and one point, you can write a linear equation in point-slope form:

#y-y_1=m(x-x_1)#,

where:

#m# is the slope, and #(x_1,y_1)# is the given point.

Plug in the known values.

#y-7=7/15(x-(-1))#

Simplify.

#y-7=7/15(x+1)#

You can convert the point-slope form to slope-intercept form by solving for #y#. #(y=mx+b)#

#y=7/15x+7/15+7#

Multiply #7# by #15/15# to get an equivalent fraction with the denominator #15#.

#y=7/15x+7/15+7xx15/15#

#y=7/15x+7/15+105/15#

#y=7/15x+112/15# #larr# slope-intercept form

graph{y-7=7/15(x+1) [-10.04, 9.96, 1.44, 11.44]}