Question

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

Answer 1

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

Answer 2

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

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

$\frac{9-7}{6-3}=\frac{2}{3}$

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:

$y=\frac{2}{3}x+c \\ 7=\frac{2}{3}(3)+c \\ 7=2+c \\ c=5$

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

$y=\frac{2}{3}x+5$

The answer is B.