A linear function has an x-intercept of 12 and a slope of 3/8. How does this function compare to the linear function that is
represented by the table?

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

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

Step-by-step explanation:

y = mx + b

m = 3/8

b = 12

y = (3/8)x + 12

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Data in the table:  slope is the rise (y) over the run (x) between two points (assuming the data represent a linear line).

 Change in x and y between two points.  I'll choose (-2/3,-3/4) and (1/3,-3/8).

Change in y:  (-3/8 - (-3/4)) = (-3/8 - (-6/8))  =  3/8

Change in x:  (1/3 - (-2/3)) = (1/3+2/3) = 3/3 = 1

Slope = (Change in y)/(Change in x) = (3/8)/1 = 3/8

The slope of the equation is the same as the data in the table.

Now let's determine if the y-intercept is also the same (12).  The equation for the data table is y = (2/3)x + b, and we want to find b.  Enter any of the data points for x and y and then solve for b.  I'll use (-2/3, -3/4)

y = (3/8)x + b

Use (-2/3, -3/4)

-3/4 =- (3/8)(-2/3) + b

-3/4 = (-6/24) + b

b = -(3/4) + (6/24)

b = -(9/12) + (3/12)

b = -(6/12)

b = -(1/2)

The equation of the line formed by the data table is y = (3/8)x -(1/2)

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