Let f(x)=2/3x+4 and g(x)=kx+6 . For which value of 𝑘 will the x-intercept of f(𝑥) be equivalent to the x-intercept of g(𝑥)?

Answer 1

0=(2/3)x +4

multiply by 3

0=2x +12

x =-6

(2/3)x +4 =0

2x +12 = 0

x =-6 = the x intercept

(2/3)x + 4 = kx +6

(2/3- k)x = 2

multiply by 3

(2-3k)x = 6

(2-3k)(-6) = 6

2-3k =-1

3k= 3

k = 1 makes the 2nd equation have the same x intercept = -6 or the point (-6,0)