How do you find the standard, point-slope, and slope intercept forms given m= -4/3, b=5/3?

1 Answer
Mar 24, 2018

Answer:

Slope Intercept Form
#y=-4/3x+5/3#
Point-Slope Form
#y-5/3=-4/3(x-0)#
Standard Form
#4x+3y=5#

Explanation:

Slope Intercept Form
#y=mx+b#
#y=-4/3x+5/3#
Point-Slope Form
#y-y_1=m(x-x_1)#
We know that the #y#-intercept is #(0,5/3)#, so we already know a point on the line.
#y-5/3=-4/3(x-0)#
Standard Form
#ax+by=c#
We can start off by using slope-intercept form, and then just solve for the constant (the integer).
#y=-4/3x+5/3#
#4/3x+y=5/3# add #4/3# to both sides
#4x+3y=5# Multiply the whole equation by 3 to achieve integer coefficients for every term (which is what standard form calls for)