SOLUTION: Determine the algebraic rule for the line that: satisfies f(0) = -2 and f(4) = 5

Question 124962This question is from textbook Intermediate Algebra Review
: Determine the algebraic rule for the line that:
satisfies f(0) = -2 and f(4) = 5 This question is from textbook Intermediate Algebra Review

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since f(0) = -2, we have the first point (0,-2). Also, because f(4) = 5, we have the second point (4,5)

So let's find the equation of the line that goes through (0,-2) and (4,5)

First lets find the slope through the points (,) and (,)

Start with the slope formula (note:

is the first point (,) and

is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

So the slope is

------------------------------------------------

Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and

is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Rewrite as

Distribute

Multiply and to get . Now reduce to get

Subtract from both sides to isolate y

Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line which goes through the points (,) and (,) is: (note: in function notation the equation is )

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer.
RELATED QUESTIONS
Determine the algebraic rule for the line that: contains (1/2, 3) and (2,... (answered by jim_thompson5910)

Suppose the polynomial f(x) is of degree 3 and satisfies f(3) = 2, f(4) = -4, f(5) = 6,... (answered by CPhill)

Find a function f that satisfies the conditions. f ''(x) = x2, f '(0) = 4, f(0) = (answered by user_dude2008)

I am having a hard time understanding what this question is asking for and what I am... (answered by scott8148)

Determine the algebraic rule for the line that contains (5,0) and is perpendicular to... (answered by richwmiller)

linear functions that satisfies the given conditions: f(0)= 2,... (answered by stanbon,solver91311)

Sketch the graph of the function f(x) that satisfies f'(x)>0 for x<-2 and x>3 and f'(x)<0 (answered by Edwin McCravy)

If f is a polynomial of degree 4 such that f(0) = f(1) = f(2) = f(3) = 1 and f(4) = 0, (answered by math_helper)

Find the formula for the exponential function that satisfies the given conditions.... (answered by Fombitz)