How do you graph #y=x/3+1#?

2 Answers
Apr 8, 2018

See below !

Explanation:

It's linear as you see the power of #x# first degree

GET

x-intercept when y=0

#x=-3#

#(-3,0)#

y-intercept when x=0

#y=1#

#(0,1)#

SO,

Take the two point and draw a straight line.

Apr 8, 2018

Please read the explanation.

Explanation:

#" "#
Given:

Linear equation #color(red)(y = x/3 + 1#

Steps:

(1) Graph the Parent Function: #color(blue)(y=x#

(2) Graph the function #color(green)(y=x/3#

(3) Graph the given function #color(red)(y=x/3 + 1#

(4) Reflection

#color(black)("Step 1"#

Graph the Parent Function: #color(blue)(y=x#

enter image source here

Observe that the linear equation goes through the origin #(0,0)#

#color(black)("Step 2"#

Graph the function #color(green)(y=x/3#

enter image source here

Observe that the linear equation goes through the origin #(0,0)# as well similar to the parent function.

#color(black)("Step 3"#

Graph the given function #color(red)(y=x/3 + 1#

enter image source here

Observe the following:

(a) x-intercept is at #(-3,0)#

(b) y-intercept is at #(0,1)#

#color(black)("Step 4"#

We will view all the graphs together and reflect on the behavior of the given function #color(red)(y = x/3 + 1#.

enter image source here

Reflection:

(a) Graph of the function #color(green)(y=x/3# and the graph the given function #color(red)(y=x/3 + 1# form parallel lines.

(b) Graph of the given function #color(red)(y=x/3 + 1# is a vertical shift of #"1 unit"# on the y-axis from the origin: #(0,0)#.

Hope you find this solution helpful.