Write a linear function f with the values f(−2)=3 and f(5)=7. A function is f(x)=

Question

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Answer 1

Since f(-2) = 3, then (-2,3) is one point of the straight line.

And, f(5) = 7 implies (5,7) is another point on the straight line.

A straight line can be defined as : Y = MX + B where M is the SLOPE, or RISE OVER THE RUN,

and B is the Y-INTERCEPT(X is zero). This is named the "SLOPE-INTERCEPT FORMULA".

Let's determine the slope by using the two points from above:

The SLOPE M = RISE/RUN = (7 - 3)/5 - (-2)) = 4/7.

Now, we need to determine the value of B, the Y-INTERCEPT.

Let's use the point (5,7) to plug into the formula Y = MX + B.

7 = ((4/7) * 5) + B

7 = 20/7 + B

7 - (20/7) = B

(49/7) - (20/7) = B

29/7 = B

Since we know the SLOPE is 4/7, and the Y-INTERCEPT is 29/7,

the SLOPE-INTERCEPT FORMULA defining the line is:

Y = (4/7)X + (29/7)

If you wanted to eliminate the fractions, you could multiply the entire equation by 7.

7Y = 4X + 29.

CHECKING:

Does 7Y = 4X + 29?

Use the point (5,7).

7Y = 49

4X + 29 = 20 + 29 = 49

49 = 49

Answer 2

The notation f(x)=y is a way to represent (x,y). So there are to point (-2,3) and (5,7). A linear function has the format of y=mx+b with m being the slope and b being the y-intercept. To find the slope use the formula (y2-y1)/(x2-x1) commonly referred to as rise over run. (7-3)/(5--2)=4/7. Now y = 4/7x+b. To find b plug in one of the points so 7=4/7(5)=b.

Some algebra

49/7=20/7+b

b=29/7

The function that satisfies these conditions is y=4/7x+29/7