What is the equation of the line with slope # m= 7/25 # that passes through # (47/5 32/10) #?

2 Answers

#y=7/25x+71/125#

Explanation:

Given:

#P_1(x_1;y_1)#

The equation of a line through a point is:

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

#:.y-32/10=7/25*(x-47/5)#

#y=7/25x-329/125+color(green)cancel(32)^color(green)16/color(green)cancel(10)^color(green)5#

#y=7/25x+(-329+400)/125#

#y=7/25x+71/125#

Jan 20, 2016

The equation in slope-intercept form is #y=7/25x+71/125#.

Explanation:

We can use the slope-intercept form of a straight line, #y=mx+b#, where slope, #m# is #7/25#, #x=47/5#, and #y=32/10#.

Notice that we don't know the y-intercept, #b#. Rearrange the equation to isolate #b#, substitute the given values and solve.

#y=mx+b#

#b=y-mx#

#b=32/10-(7/25)(47/5)#

Simplify.

#b=32/10-(329)/(125)#

Simplify #32/10# to #16/5#.

#b=16/5-329/125#

The LCD is #125#. Multiply #16/5# times #25/25#.

#b=16/5(25/25)-329/125#

Simplify.

#b=400/125-329/125#

Simplify.

#b=71/125#

The equation in slope-intercept form is #y=7/25x+71/125#.