What is thelinear function whose graph has the points (-4,0) and (1,3)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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:

 f(x)=y 

f(-4)=a*(-4)+b

But f(-4)=0,

a*(-4)+b = 0

-4a + b = 0

4a = b (1)

We'll do the same for the point (1,3):

 f(1)=a*(1)+b

But f(1)=3,

a*(1)+b=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

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