Question

Write the equation of the line that passes through the points (1, 7) and (5, 15) using function notation.
A. y= 2x + 5
B. y= 4x + 8
C. f(x)= 2x + 5
D. f(x)= 4x + 8
Please I need help!

Answer 1

We can find the slope of the line by using the slope formula:

\[\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\]

Substituting the data you are given:

\[\frac{15 -7 }{5 - 1 }\]
\[\frac{8}{4}\]

Since we know that 8 divided by 4 is 2, we know the slope of the line is 2.

The only other piece of information we need is the y-intercept of the function, which we can find by using the slope. We know that when "x" is increased by 1, "y" increases by two. Therefore, we know that when "x" is decreased by one, instead, "Y" is decreased by two.

One of the points you are given is (1, 7). If we subtract one from "x" and two from "y", we get the point (0, 5). Since "x" is now equal to zero, we know that the y-coordinate, or 5, is the y-intercept.

These two pieces of information cancel out answers B and D, since they have the wrong slope. Since the answer also had to be written in function notation, not "y =" form, answer A cannot be correct, either. This leaves us with only answer C to be correct.

Hope I helped, and let me know if you have any questions :D