Question 1005035
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.