Question

Which function passes through the points (2, 3) and (4, 4)?

Answer 1

The function that passes through the points (2, 3) and (4, 4) is y = 1/2x + 2.

Step-by-step explanation:

The function that passes through the points (2, 3) and (4, 4) can be found using the point-slope formula.

First, we find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the two points, we get:

m = (4 - 3) / (4 - 2) = 1 / 2

Next, we use the slope-intercept form (y = mx + b) and substitute one of the given points to find the y-intercept (b). Let's substitute (2, 3):

3 = (1 / 2) * 2 + b
3 = 1 + b
b = 2

Therefore, the function that passes through the points (2, 3) and (4, 4) is y = 1/2x + 2.

Answer 2

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