Which function passes through the points (2, 3) and (4, 4)?
point -slope form of a straight:
we have a point (x₀,y₀) and the slope m.
y-y₀=m(x-x₀)
Given two points (x₁,y₁) and (x₂,y₂) the slope will be:
m=(y₂-y₁)/( x₂-x₁) or m=(y₁-y₂)/(x₁-x₂)
In this case:
(2,3)
(4,4)
m=(4-3) / (4-2)=1/2
we can choose the point (2,3) or the point (4,4); the result will be the same.
y-y₀=m(x-x₀)
y-4=1/2(x-4)
y=1/2 x-2+4
y=1/2 x + 2
Answer: the funciton passes through the poinsts (2,3) and (4,4) is:
y=1/2 x+2
Function passes through the points \(\boldsymbol{(2,3)}\,,\boldsymbol{(4,4)}\) is \(\boldsymbol{x-2y+4=0}\)
A function is a relation in which each and every element in a domain has a unique image in the co-domain.
Let the given points be as follows:
\(\boldsymbol{(x_1,y_1)=(2,3)}\\\boldsymbol{(x_2,y_2)=(4,4)}\)
Function passing through points \((x_1,y_1),(x_2,y_2)\) is given as follows:
\(\boldsymbol{y-y_1=\left ( \frac{y_2-y_1}{x_2-x_1} \right )(x-x_1)}\)
\(y-3=\left ( \frac{4-3}{4-2} \right )(x-2)\)
\(y-3=\frac{1}{2}(x-2)\)
\(2y-6=x-2\)
\(\boldsymbol{x-2y+4=0}\)
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