Which equation is in slope-intercept form and represents a line with slope 3 through the point (9, –4)?

Question

Which equation is in slope-intercept form and represents a line with slope 3 through the point (9, –4)?

Answer 1

When a point and slope are given, one can use the point-slope form:

 

m(x -  x₁) = (y - y₁)

3(x - 9) = (y - (-4))

3x - 27 = y + 4

3x - 31 = y

 

y = 3x - 31

Answer 2

The slope-intercept form of the equation of a line looks like this:

                y = mx + b      (where m is the slope and b is the y-intercept -- the value of y when x=0)

 

The problem gives the slope, so we have:  y = 3x + b

 

Then the problem gives a point in the form (x,y), which is (9,-4), so that we can solve for b.

         -4 = 3(9) + b       [ put values for (9,-4) into our equation ]

         -31 = b                  [ subtract 27 from both sides]

 

Check (very important):

   Is the point (9,-4) on the line  y = 3x - 31     ??

                                -4 = 3*9 - 31     ?

                               -4  =  -4             yes.