Write the slope -intercept form of the equation of the line through the given point with the given slope.

Question

through: (3,-1), slope = 2/3

 

through: (3,-5), slope = undefined

Answer 1

For another approach re the first one, using the y-intercept form:
y = mx + b

We know m (the slope) is 2/3
We also know one set of x/y pairs since we're given (3,-1)
So, substituting, we get:

y = m*x + b
-1 = 2/3*(3) + b
-1 = 2 + b
-1 - 2 = b
-3 = b

Now that we have b, and were given m, we get:

y = m*x + b
y = 2/3*x - 3

 

- Greg, from Queens, nearby Brooklyn

Answer 2

Hello, Cynthia

 

1) m= 2/3   point(3,-1)

Start by using the point-slope form

 

y-y1  = m (x- x1),                          where x1=3, y1=-1, m= 2/3

y-(-1)= 2/3( x-3).                          substituting

y+1=   2/3( x-3).                            Multiply both sides by 3

3(y+1)= 3[2/3 (x-3)]

3y+3   = 2(x-3)                              Note: 3(2/3)= 6/3= 2

3y+3   = 2x-6                                Using the distributive property

    -3          -3                                 Subtracting 3 from both sides

       3y= 2x-9                                 Dividing both sides by 3

        y= (2/3)x-3                            This is the slope-intercept form

 

2) m= undefined.  (3, -5) .  Since the slope is undefined this must be a vertical line that passes through point (3,-5). So, the equation of this line is x=3.  Don't forget this.  Any vertical line will be x= the x-coordinate that it passes through.  

 

I hope this helps out and thanks for posting.

D.Y. T.

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