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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