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 a different y-intercept.
It has the same y-intercept and a different slope.
It has a different slope and a different y-intercept

The correct option is;

It has the same slope and a different y-intercept

Step-by-step explanation:

The data on the table can be presented as follows;

x             y

-2/3       -3/4

-1/6        -9/16

1/3         -3/8

5/6       -3/16

The rate of change of the function, m = (-3/16 - (-3/4))/(5/6 - (-2/3)) = 3/8

The equation of the line given by the data points in point and slope form is given as follows;

y - (-3/16) = 3/8×(x - 5/6)

y = 3·x/8 - 5/16 - 3/16 = 3·x/8 - 1/2

y = 3·x/8 - 1/2

The y intercept is given at when x = 0, therefore, at the y-intercept, y = 3 × 0/8 - 1/2 = -1/2

The y-intercept is (0, -1/2)

The x-intercept occurs at y = 0, therefore, at the x-intercept, we have;

0 = 3·x/8 - 1/2

∴ 3·x/8 = 1/2

x = 4/3

Therefore, the x-intercept is 4/3 and the coordinates of the x-intercept is (4/3, 0)

Given that the x-intercept is different, the y-intercept of the two lines with the same slope are also different

The correct option is therefore that it has the same slope and a different y-intercept;

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