What is thelinear function whose graph has the points (-4,0) and (1,3)?
The linear function whose graph passes through (-4 , 0) and (1, 3) is the equation of the line passing through the two points.
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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