The equation #3x+1.5y = 30# describes the number of burgers and hot dogs a family can buy with $30. What are the intercepts of the equation, and what does each represent?

3 Answers
Jun 27, 2018

Basically the intercepts represent the number of one of the items you can buy using the entire amount of #$30#.

Explanation:

Have a look:
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Jun 27, 2018

See a solution process below:

Explanation:

#x#-intercept: To find the #x# intercept set #y# to #0# and solve for #x#:

#3x + (1.5 xx 0) = 30#

#3x + 0 = 30#

#3x = 30#

#(3x)/color(red)(3) = 30/color(red)(3)#

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

#x = 10# or #(10, 0)#

#y#-intercept: To find the #y# intercept set #x# to #0# and solve for #x#:

#(3 xx 0) + 1.5y = 30#

#0 + 1.5y = 30#

#1.5y = 30#

#(1.5y)/color(red)(1.5) = 30/color(red)(1.5)#

#(color(red)(cancel(color(black)(1.5)))y)/cancel(color(red)(1.5)) = 20#

#y = 20# or #(0, 20)#

The intercepts represent the maximum number of hotdogs or hamburgers the family could by,

So for example, if they bought no hotdogs (the y value equal to 0) they could buy 10 hamburgers, the #x#-intercept.

Jun 27, 2018

x intercept represents #10# burgers only can be bought in #$30# , y intercept represents #20# hot dogs only can be bought in #$30#

Explanation:

#3 x+ 1.5 y=30#

Let # x# be the number of burgers of #$3# cost per unit

and # y# be the number of hot dogs of #$1.5# cost per unit

x intercept is found by putting #y=0# in the equation.

# 3 x +1.5*0=30 or 3 x = 30 or x= 10# , It reveals that

#10# burgers alone can be bought in #$30#

y intercept is found by putting #x=0# in the equation.

# 3*0 +1.5 y=30 or 1.5 y = 30 or y= 30/1.5=20# , It reveals

that #20# hot dogs alone can be bought in #$30#

x intercept represent #10# burgers only can be bought in #$30#

y intercept represent #20# hot dogs only can be bought in #$30#

graph{3 x+1.5 y=30 [-80, 80, -40, 40]} [Ans]

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