Question

A line passes through (3, 7) and (6, 9). Which equation best represents the line?

A y = 3 over 2x + 5
B y = 2 over 3x + 5
C y = 3x + 2
D y = 2 over 3x + 2

Answer 1

Let's recall the equation to find out the slope of a line:


`(y_(2)-y_(1))/(x_(2)-x_(1))`

Next, we substitute our given values into the equation, and simplify:


`(9-7)/(6-3)=(2)/(3)`

Now, we insert the slope (2/3) into the y=mx+b equation and substitute the values from one of the coordinates to find what b, the y-intercept is:


`y=(2)/(3)x+c \\ 7=(2)/(3)(3)+c \\ 7=2+c \\ c=5`

So, the y-intercept is 5. We can now put our discovered values for the slope and the y-intercept into one equation:


`y=(2)/(3)x+5`

The answer is B.

Answer 2

The name is the second option y= (2/3)x +5. Hope this helps