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;

step-by-step explanation:

consider an orange peel: if you want to try and lay it flat, you have to stretch it, we know exactly how things are being stretched or squashed at any given point. we have many different map projections because each has different patterns of some projections can even preserve certain features of the earth without