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How do you put f(-2)=1 and f(-1)=3 in slope-intercept form?

I have this question as part of my Pre-Calc summer work. I never learned about f(x) equations without the variable x in them... it just doesn't make sense to me based on what I know. Please help! I need to turn this thing in today if possible..

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Katherine P. | Experienced Math and Test Prep TutorExperienced Math and Test Prep Tutor
5.0 5.0 (572 lesson ratings) (572)

Let's just think of f(x) as another way to refer to y

f(x) = y

f(-2) = 1, is telling you that when x = -2, y = 1

f(-1) = 3, is telling you that when x = -1, y = 3

So they're giving you 2 points and asking you to find the equation of the line.

(-2, 1) (-1, 3)

To go from here, you can find the slope (change in y over change in x) and then write out the equation using point-slope form. Lastly, rearrange into slope intercept form and you're all set.

Check out this site of an example and step by step directions:


This was great thank you so much for this it helped me a lot on my school unit.
I'm glad it helped! Thanks for your comment :)
Mike C. | Enthusiastic Tutor for Middle and High School StudentsEnthusiastic Tutor for Middle and High S...
4.8 4.8 (82 lesson ratings) (82)

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If we know the positions of two points on a line, then we can know both the line's slope and y-intercept. Let me explain.

So you've got two points on the line, (-2, 1) and (-1, 3). We can calculate the slope by rise over run, so m = (3 - 1)/((-1) - (-2)) or 2. To get b, we can plug the x- and y-values of either point; say we do it for the first point, then what we get is 3 = 2(-1) + b; from this, we can get that b = 5.

Hence the line's equation is y = 2x + 5.

Imtiazur S. | Tutor with masters degree and experience teaching CalculusTutor with masters degree and experience...
4.9 4.9 (343 lesson ratings) (343)

I like the previous answer.  Alternatively...

the slope intercept form for a straight line is y=mx+b (m is slope and b the y intercept)

This can also be written as f(x)=mx+b by convention.  f(-2)=-2m+b.  



Solving the system of equations for m and b we get 

m=2 and b=5

Brad M. | STEM Specialist plus Business, Accounting, Investment & EditingSTEM Specialist plus Business, Accountin...
4.9 4.9 (233 lesson ratings) (233)

Hi Kylie!

"f(-2) means we're using x= -2 ... thus f(-2)=1 lands at the point (-2,1), f(-1)=3 lands at (-1,3) ... looks like the "rise over run" is 2/1 or slope m= 2 ... find b: 1= 2(-2) +b ... b=5 ... y= 2x +5 works ... Regards :)