Question 19192
Recall that the slope-intercept form of the equation for a line is:  y = mx+b where m is the slope and b is the y-intercept.

First, find the slope using the two given points:
 {{{m = (y2-y1)/(x2-x1)}}}
(x1, y1) = (1, 5)
(x2, y2) = (2, 7)

{{{m = (7-5)/(2-1)}}}
{{{m = 2/1}}}
{{{m = 2}}} So now you can write: {{{y = 2x + b}}} but you need to find the value of b, the y-intercept.
Use the x- and y-coordintes of any one of the two given points, substitute these into the above equation and solve for b. Using the first point (1, 5),

{{{5 = 2(1) + b}}} Subtract 2 from both sides.
{{{3 = b}}}

Now you can write the final equation:

{{{y = 2x + 3}}}