How do you write an equation in point slope form given slope 2/3, (5,6)?

1 Answer
Sep 3, 2016

The linear equation in point slope form is #y-6=2/3(x-5)#.

Explanation:

The general equation for a line in point slope form is #y-y_1=m(x-x_1)#, where #m="slope"=2/3"#, #x_1=5#, and #y_1=6#.

To get the point slope form for the variables given, plug the known values into the equation.

#y-6=2/3(x-5)#

________

Now, if you wish, you can determine the slope intercept form for easier graphing, by solving the point slope form for #y#. This will give the x and y interceptss, where the x-intercept is the value of #x# when #y=0#, and the y-intercept is the value of #y# when #x=0#. Once you have the x and y intercepts, you only need to plot two points to graph the line.

The general equation for the slope intercept form is #y=mx+b#, where #m# is the slope, #(2/3)#, and #b# is the y-intercept.

Start with the point slope form and solve for #y#.

#y-6=2/3(x-5)#

Add #6# to both sides.

#y=2/3(x-5)+6#

Simplify.

#y=2/3x-10/3+6#

Multiply #6# by #3/3# to get #18/3#.

Simplify.

#y=2/3x-10/3+18/3#

Simplify.
The slope intercept form is #y=2/3x+8/3#, where the slope, #m#, is #2/3#, and the y-intercept is #8/3# and the point is #(0,8/3)#.

To find the x-intercept , make #y=0# and solve for #x#.

#0=2/3x+8/3#

#-2/3x=8/3#

#-6x=24#

#x=24/(-6)#

#x=-4#

The x-intercept is #-4# and the point is #(-4,0)#.

graph{y=2/3x+8/3 [-10, 10, -5, 5]}