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)y6=23(x5).

Explanation:

The general equation for a line in point slope form is y-y_1=m(x-x_1)yy1=m(xx1), where m="slope"=2/3"m=slope=23, x_1=5x1=5, and y_1=6y1=6.

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

y-6=2/3(x-5)y6=23(x5)

________

Now, if you wish, you can determine the slope intercept form for easier graphing, by solving the point slope form for yy. This will give the x and y interceptss, where the x-intercept is the value of xx when y=0y=0, and the y-intercept is the value of yy when x=0x=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+by=mx+b, where mm is the slope, (2/3)(23), and bb is the y-intercept.

Start with the point slope form and solve for yy.

y-6=2/3(x-5)y6=23(x5)

Add 66 to both sides.

y=2/3(x-5)+6y=23(x5)+6

Simplify.

y=2/3x-10/3+6y=23x103+6

Multiply 66 by 3/333 to get 18/3183.

Simplify.

y=2/3x-10/3+18/3y=23x103+183

Simplify.
The slope intercept form is y=2/3x+8/3y=23x+83, where the slope, mm, is 2/323, and the y-intercept is 8/383 and the point is (0,8/3)(0,83).

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

0=2/3x+8/30=23x+83

-2/3x=8/323x=83

-6x=246x=24

x=24/(-6)x=246

x=-4x=4

The x-intercept is -44 and the point is (-4,0)(4,0).

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