Can you please help me with an Algebra question?

Question

Ok, I have an algebra review for geometry homework that's due on the 1st day of school. On one page, it reviews over writing equations of a line and I'm stuck on a problem. The problem is:

f(1)= -2,

f(2)= 1,

y-int. is -5

How would I solve that?

Thank you so much!!!

Answer 1

The equation of the line should satisfy 3 conditions; that's

f(1) = 2 ==> the line passes  the point (1, -2)   (condition 1)

f(2) = 1 ==> the line passes the point (2, 1)      (condition 2)

therefore the slope 2 points is:

a = (1 - (-2))\(2 - 1) = 3/1 = 3

y - int is -5 that is the line passes the point (0, 5) (condition 3)

Combine the slope and y-int point, the line is



y = 3x - 5    is the answer.

Answer 2

The general equation for a straight line is:

y = ax + b

Since the line goes through (1, -2), you have:

-2 = a + b

And since it goes through (2, 1), you have:

1 = 2a + b

Subtract the first equation from the second to get rid of b:

3 = a

Therefore a = 3. But 1 = 2a + b => 1 = 6 + b => -5 = b.

So the equation is y = 3x - 5