Mathematics: A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to the linear function that is represented by the table? x y Negative two-thirds Negative three-fourths Negative one-sixth Negative StartFraction 9 Over 16 EndFraction One-third Negative StartFraction 3 Over 8 EndFraction StartFraction 5 Over 6 EndFraction Negative StartFraction 3 Over 16 EndFraction It has the same slope and the same y-intercept. It has the same slope and

that’s the pictureStep-by-step explanation:...

A linear function has an x-intercept of 12 and - id127056317, CoreyHammond584

Ответ:

sierravick123owr441

30.01.2022

Mathematics

(B) It has the same slope and a different y-intercept

Step-by-step explanation:

The table is presented below:

$\left|\begin{array}{c|c}x&y\\----&---\\-\frac{2}{3} &-\frac{3}{4}\\\\-\frac{1}{6}&-\frac{9}{16}\\\\\frac{1}{3}&-\frac{3}{8}\\\\\frac{5}{6}&-\frac{3}{16}\end{array}\right|$

Gradient

$m=\dfrac{-\frac{3}{8}-(-\frac{3}{4})}{\frac{1}{3}-(-\frac{2}{3})}\\=\dfrac{-\frac{3}{8}+\frac{3}{4}}{\frac{1}{3}+\frac{2}{3}}\\=\frac{3}{8}\div \frac{3}{3}\\m=\frac{3}{8}$

Next, we determine its y-intercept

Using the pair $(-\frac{2}{3},-\frac{3}{4})$ in y=mx+b

$-\frac{3}{4}=(\frac{3}{8})(-\frac{2}{3})+b\\-\frac{3}{4}+\frac{1}{4}=b\\b=-\frac{1}{2}$

Comparing with the linear function has an x-intercept of 12 and a slope of $\frac{3}{8}$ , we find out that It has the same slope and a different y-intercept.

Option B is the correct option.

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