Question

Write an equation for a function that includes the given pair of points (1,2) and (2,4).

a) (y = 2x)
b) (y = x + 1)
c) (y = 2x + 1)
d) (y = x^2)

Answer 1

The equation that includes the given pair of points (1,2) and (2,4) is y = 2x, which is option a.

Step-by-step explanation:

To determine which function includes the given pair of points (1,2) and (2,4), we can test each option by substituting the x-values from the points to see if we get the corresponding y-value.

For option a) y = 2x, when x=1, y=2(1)=2, which matches the first point. When x=2, y=2(2)=4, which matches the second point.

For option b) y = x + 1, when x=1, y=1+1=2, which matches the first point. When x=2, y=2+1=3, which does not match the second point.

For option c) y = 2x + 1, when x=1, y=2(1)+1=3, which does not match the first point.

For option d) y = x^2, when x=1, y=1^2=1, which does not match the first point.

Therefore, the equation that perfectly fits the given pair of points is y = 2x (option a).