How do you find the x and y intercepts of #3x-4y-10=0#?

2 Answers
Mar 25, 2017

Answer:

The intercepts are at #(3 1/3, 0) and (0,-2 1/2)#

Explanation:

Finding the intercepts is a very easy and very useful skill to develop for drawing graphs. It is particularly handy for linear programming.

All along the #x#-axis, #y=0# All points are #(x, 0)#

All along the #y#-axis, #x=0# All points are #(y, 0)#

To find the #x#-intercept, set #y=0# and solve for #x#

To find the #y#-intercept, set #x=0# and solve for #y#

The only time this does not work is if the graph goes through the origin.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#3x-4y-10 =0" "rarr 3x -4y =10#

For the #x#-int: #y=0#
#" "3x -4(0) = 10" "rarr3x=10" "x= 3 1/3#

For the #y#-int: #x=0#
#" "3(0) -4y = 10" "rarr-4y=10" "y= -5/2#

The intercepts are at #(3 1/3, 0) and (0,-2 1/2)#

Mar 25, 2017

Answer:

The x-intercept is #(10/3, 0)=(3 1/3,0)#.

The y-intercept is #(0,-5/2)=(0, -2 1/2)#

See the explanation for the process.

Explanation:

Find x and y intercepts. The x-intercept is the point where #y# is #0#. The y-intercept is the point where #x# is #0#.

Given

#3x-4y-10=0#

X-intercept

Substitute #0# for #y#.

#3x-4(0)-10=0#

Simplify.

#3x-10=0#

Add #10# to both sides.

#3xcolor(red)cancel(color(black)(-10))+color(red)cancel(color(black)(10))=0+10#

Simplify.

#3x=10#

Divide both sides by #3#.

#color(red)cancel(color(black)(3)color(black) x)/color(red)cancel(color(black)(3))=10/3#

#x=10/3#

The x-intercept is #(10/3, 0)=(3 1/3,0)#.

Y-intercept

Substitute #0# for the #x#. Solve for #y#.

#3(0)-4y-10=0#

Simplify.

#-4y-10=0#

Add #10# to both sides.

#-4y=10#

Divide both sides by #-4#.

#y=10/(-4)#

#y=-10/4#

Simplify.

#y=-5/2#

The y-intercept is #(0,-5/2)=(0, -2 1/2)#

Use the graph below to check the x and y intercepts.

graph{3x-4y-10=0 [-16.02, 16, -8.01, 8.01]}