Find an equation of the line that has the given slope and passes through the given point. m=-2,(4,6) the equation of the line is

Question

Find an equation of the line that has the given slope and passes through the given point.

     m=-2,(4,6)

the  equation of the line is

Answer 1

The slope-intercept form of the equation of a line looks like:   y=mx + b

      where y = slope and b is the y-intercept (the place where x=0)

 

The slope is given, so the equation is:    y = -2 +b      and we are given a point:  (4,6)

    y = -2x + b

    6 = -2(4) + b          [plug in values and solve for b]

    14 = b

 

The equation is:    y = -2x + 14

Answer 2

y = -2x + b where b is the y intercept

 

To find the y-intercept, start with the given point (4,6).

 

If we go back 4 units in x, we must go up 8 units. Therefore the y-intercept is 6 + 8 = 14.

 

The full equation is then y = -2x + 14

 

To check, plug in x = 4: y = -2(4) + 14 = 6.