Answer:
(B) It has the same slope and a different y-intercept
Step-by-step explanation:
The table is presented below:
[tex]\left|\begin{array}{c|c}x&y\\----&---\\-\frac{2}{3} &-\frac{3}{4}\\\\-\frac{1}{6}&-\frac{9}{16}\\\\\frac{1}{3}&-\frac{3}{8}\\\\\frac{5}{6}&-\frac{3}{16}\end{array}\right|[/tex]
Gradient:
[tex]m=\dfrac{-\frac{9}{16}-(-\frac{3}{4})}{-\frac{1}{6}-(-\frac{2}{3})}\\=\dfrac{-\frac{9}{16}+\frac{3}{4}}{-\frac{1}{6}+\frac{2}{3}}\\=\frac{3}{16}\div \frac{1}{2}\\m=\frac{3}{8}[/tex]
Next, we determine its y-intercept
Using the pair [tex](-\frac{2}{3},-\frac{3}{4})}[/tex] in y=mx+c
[tex]-\frac{3}{4}=(\frac{3}{8})(-\frac{2}{3})+c\\-\frac{3}{4}+\frac{1}{4}=c\\c=-\frac{1}{2}[/tex]
Comparing with the linear function has an x-intercept of 12 and a slope of [tex]\frac{3}{8}[/tex], we find out that It has the same slope and a different y-intercept.
Option B is the correct option.
