How do you graph #3x-5y=15# using intercepts?

2 Answers
Aug 2, 2017

Answer:

See a solution process below:

Explanation:

To find the intercepts, equate one variable to #0# and solve for the other variable:

y-intercept

Set #x# to #0# and solve for #y# giving:

#3x - 5y = 15# becomes:

#(3 * 0) - 5y = 15#

#0 - 5y = 15#

#-5y = 15#

#(-5y)/color(red)(-5) = 15/color(red)(-5)#

#(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -3#

#y = -3# or #(0, -3)#

x-intercept

Set #y# to #0# and solve for #x# giving:

#3x - 5y = 15# becomes:

#3x - (5 * 0) = 15#

#3x - 0 = 15#

#3x = 15#

#(3x)/color(red)(3) = 15/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 5#

#x = 5# or #(5, 0)#

Next. we can plot the two points on the grid:

graph{((x-5)^2+(y)^2-0.125)((x)^2+(y+3)^2-0.125)=0 [-20, 20, -10, 10]}

Then, draw a line through the two points:

graph{(3x - 5y -15)((x-5)^2+(y)^2-0.125)((x)^2+(y+3)^2-0.125)=0 [-20, 20, -10, 10]}

Aug 2, 2017

Answer:

Draw a straight line through the intercept points as indicated below.

Explanation:

Note that the given equation: #3x-5y=15# is a linear (straight line) equation with:
#x#-intercept (value of #x# when #y=0#) of #x=5#
and
#y#-intercept (value of #y# when #x=0#) of #y=-3#

Therefore we have the two points:
#color(white)("XXX")(x_1,y_1)=(5,0) and (x_2,y_2)=(0,-3)#

Plotting these two points on the Cartesian plane and drawing a straight line through them should give a graph that looks like:
enter image source here