SOLUTION: write an equation for a linear function f that has the given values f(-3) =2 and f(1)=0

Question 1005035: write an equation for a linear function f that has the given values f(-3) =2 and f(1)=0

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the slope intercept form of the linear function is:

y = mx + b

m is the slope
b is the y-intercept

m = (y2-y1) / (x2-x1)

(x1,y1) is any one point on the line.
(x2,y2) is any other point on the line.

you are given that:

f(1) = 0
f(-3) = 2

f(1) = 0 means that the value of the function is equal to 0 when the value of x is equal to 1.

that tells you that your first point will be (x1,y1) = (1,0)

f(-3) = 2 means that the value of the function is equal to 2 when the value of x is equal to -3.

that tells you that your second pont will be (x2,y2) = -3,2)

now that you have two points on the line, you can find the slope.

m = (y2 - y1) / (x2 - x1) which becomes:

m = (2 - 0) / (-3 - 1) which becomes:

m = 2 / -4 which becomes:

m = -1/2

you now have your slope.

the general form of the equation of y = mx + b becomes:

y = -(1/2)x + b

all that's left is to find b, which is the y-intercept.

take any one of your known points and replace y with the y value of the coordinate and replace x with the x value of the coordinate and solve for b.

we'll use (x2,y2) = (-3,2)

your equation is y = -(1/2)x + b

replace y with 2 and replace x with -3 and the equation becomes:

2 = -(1/2)*(-3) + b

simplify to get:

2 = (3/2) + b

subtract (3/2) from both sides of the equation to get:

2 - (3/2) = b

solve for b to get:

b = 1/2

your equation is now:

y = -(1/2)x + 1/2

you're done.

y = -(1/2)x + 1/2 is the same as:

f(x) = -(1/2)x + 1/2, if you set y = f(x).

when the value of x is equal to 1, your function becomes:

f(1) = -(1/2)*1 + 1/2 which becomes:

f(1) = -1/2 + 1/2 which becomes:

f(1) = 0

when the value of x is equal to -3, your function becomes:

f(-3) = -(1/2)*(-3) + 1/2 which becomes:

f(-3) = (3/2) + 1/2 which becomes:

f(-3) = 2

the equation is modelling the straight line that goes through both your given points.

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