What is the equation of a line with slope -9 and passing through (6, 7), and how do I write it in function notation.

Question

Slope -9; through (6,7)

Answer 1

Equation of a line with slope m and point (x₁,y₁) through which it passes is:
    y-y₁=m(x-x₁)

Since the given line has a slope, m=-9 and passes through (6,7), x₁=6 and y₁=7 the equation is:
    y-7=-9(x-6) 

    y-7=-9x+54
    y=-9x+61           [add 7 to both sides]

 

Checking that the point (6,7) is on the line:

  Is   7 = -9(6) + 61   ?

        7 = -54 + 61   ?

        7 = 7   ? yes

Answer 2

Equation of a straight line with given slope, m and point (x₁,y₁) through which it passes is:

y-y₁=m(x-x₁)

Since the given line has a slope, m=-9 and passes through (6,7) i.e., x₁=6 and y₁=7 the equation should be:

y-7=-9(x-6)

=>y-7=-9x+54

=>y=-9x+43... adding 7 to both sides

Therefore the desired equation is, y=-9x+61

In function notation, y=f(x)=-9x+61