How do you graph #y=-5x+10# using intercepts?

1 Answer
Sep 28, 2017

Answer:

See a solution process below:

Explanation:

First, find the #y#-intercept by setting #x# to #0# and calculating #y#:

y-intercept:

#y = (-5 * 0) + 10#

#y = 0 + 10#

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

Next, find the #x#-intercept by setting #y# to #0# and solving for #x#:

x-intercept:

#0 = -5x + 10#

#0 - color(red)(10) = -5x + 10 - color(red)(10)#

#-10 = -5x + 0#

#-10 = -5x#

#(-10)/color(red)(-5) = (-5x)/color(red)(-5)#

#2 = (color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5))#

#2 = x#

#x = 2# or #(2, 0)#

We can next graph the two points on the coordinate plane:

graph{(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(y+5x-10)(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]}