The linear function whose graph passes through (-4 , 0) and (1, 3) is the equation of the line passing through the two points.
The equation of the line passing through (x1 , y1) and (x2, y2) is given by (y - y1) = [(y2 - y1)/(x - x2)]*(x - x1).
Substituting the values given to us we get:
(y - 0) = [( 3- 0)/(1+ 4)]*( x + 4)
=> y = (3/5)*(x + 4)
Therefore the function is
f(x) = (3x/5) + 12/5
If a point it is located on the graph of a function, it's coordinates verify the expression of the function.
The expression of a linear function is:
f(x) = mx + n
We'll substitute the coordinates of the first point in the equation of the linear function:
a*(-4)+b = 0
-4a + b = 0
4a = b (1)
We'll do the same for the point (1,3):
a + b = 3 (2)
We'll substitute (1) in (2):
a + 4a = 3
5a = 3
a = 3/5
We'll multiply by 4:
4a = b = 12/5
The linear function is:
f(x)=3x/5 + 12/5