Find an equation of the line that passes through the points

Find an equation of the line that passes through the points (-2, 5) and (-6, -7). Your final answer should give the entire formula. Show at least two steps of work. Use the table to determine whether f is a linear function, and explain. If it is linear, find a formula f(x) = mx + b to represent it. Let f (x) = 3x^2/x(x^2 + 8x + 15). Find the domain of f and show some kind of work or explanation.

Solution

1) (-2, 5) and ( -6, -7)

slope = ( -7 -5)/( -6 +2) = -12/-4 = 3

slope intercept form : y = mx +c

y = 3x +c ; 5 = -6 +c

c = 11

y = 3x +11

2) If the data given is linear check the slope , m = (y2 -1 y1)/(x2 - x1)

x ---- f(x)

-1 ---- -7

1 ----- 9 ---> m1 = ( 9+7)/(1+1) =8

4 ----- 33 ----> m2 = (33 -9)/(4 -1) = 8

Its a linear function

f(x) = mx +b ; f(x) = 8x +b

Use (1, 9) to find b : 9 = 8 +b

b = 1

So, f(x) = 8x +1