How do you find the x and y intercepts for # y=3x-2 #?

2 Answers
Jan 22, 2016

Answer:

#y = - 2# and #x = 2/3 #

Explanation:

This is the equation of a straight line. When the line crosses the x-axis the y-coordinate will be zero. By Putting #y = 0# we can find the corresponding value of x (the x-intercept ).

Put #y = 0# : #3x - 2 = 0# so #3x = 2 ## rArr x = 2/3 #

Similarly , when the line crosses the y-axis the x-coordinate will be zero. Put #x = 0# to find the y-intercept.

Put #x = 0# : #y= 0 - 2# #rArry=-2#

Jan 22, 2016

Answer:

#color(blue)(" y-intercept"->y=-2)#
#color(blue)(" x-intercept"->x=2/3_#

Explanation:

Given:#color(white)(.....) y=3x-2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the x-intercept")#

This is a strait line graph so you will find that the plotted line crosses the y-axis (intercept) at the same value as the constant of #-2#

Why is this?

The y-axis crosses the x-axis at #x=0#. That means that the plot also crosses (intercept) the y-axis at #x=0#. So if we substitute #x=0# into the equation we get:

#y=(3xx0)-2#

#color(blue)("y-intercept"->y=-2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the x-intercept")#

By the same logic, the plotted line crosses (intercept) the x-axis at y=0. So if we substitute #y=0# into the equation then we have:

#y=3x-2color(white)(.x..) -> color(white)(.x..)color(brown)(0=3x-2)#

Add #color(blue)(2)# to both sides:

#color(brown)(0color(blue)(+2)=3x-2color(blue)(+2))#

#color(green)(2=3x+0)#

Divide both sides by #color(blue)(3)#

#color(green)(2/(color(blue)(3))=(3x)/(color(blue)(3))#

#2/3=3/3xx x#

But 3/3 = 1 giving:

#2/3=x#

#color(blue)("x-intercept"->x=2/3_#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~