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

Question

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

Ethan Adkins · Accepted Answer

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

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.

Ethan Adkins · Answer

Convert the equation to standard form

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]}

Eli Assouline · Answer

undefined To graph the equation $ y = \frac{3}{2}x + 3 $:

1. Identify the y-intercept: The y-intercept occurs when $ x = 0 $. Substitute $ x = 0 $ into the equation to find the y-intercept, which is $ (0, 3) $.

2. Identify the slope: The coefficient of $ x $ represents the slope. In this case, the slope is $ \frac{3}{2} $.

3. Use the slope and y-intercept to plot a second point: Starting from the y-intercept, move up 3 units (since the numerator of the slope is 3) and then move right 2 units (since the denominator of the slope is 2) to find a second point, which is $ (2, 6) $.

4. Plot the two points $ (0, 3) $ and $ (2, 6) $ on the coordinate plane.

5. Draw a straight line passing through the two points to represent the graph of the equation.