How do you graph #y=3/2 x + 3#?

2 Answers
Jun 8, 2018

Start with the point ( 0 + 3) then go up 2 and over 3 to point ( 3,5) connect the dots.

Explanation:

The equation is in the slope intercept form which makes this easy

# y = mx + b#

where m = the slope ( think mountain ski slope)
and b = the y intercept ( think beginning.)

Start at b the beginning

b = ( 0 +3) b is the y intercept where x = 0 and y = 3

Then use the slope # 2/3 = y/x#

Add 2 to the y value # 3 + 2 = 5 #
Add 3 to the x value # 0 + 3 = 3 #

this gives the second point ( 3,5)

plot the two points and connect the dots with a line, The graph of the equation is done.

Jun 8, 2018

Convert the equation to standard form

Explanation:

Graph:

#y=3/2x+3#

You need two points to graph a straight line. The x- and y-intercepts are easiest to find, especially when the equation is in standard form.

Convert to standard form, #Ax+By=C#, by subtracting #3/2x# from both sides.

#-3/2x+y=3#

X-intercept: value of #x# when #y=0#

Substitute #0# for #y# and solve for #x#.

#-3/2x+0=3#

#-3/2x=3#

Multiply both sides by #2#.

#-3x=3xx2#

#-3x=6#

Divide both sides by #-3#.

#x=6/(-3)#

#x=-2#

The x-intercept is: #(-2,0)#.

Y-intercept: value of #y# when #x=0#

Substitute #0# for #x# and solve for #y#.

#-3/2(0)+y=3#

#y=3#

The y-intercept is: #(0,3)#.

Plot the x- and y-intercept and draw a straight line through them.

graph{y=3/2x+3 [-10, 10, -5, 5]}