It is simple enough to graph a line that will pass through the point (x = 7, y = 5) given a slope of 3. Using the standard equation for a line in the form of

**y =
mx + b**

where m is the slope and b is the y-intercept.

**____________________**

We would have the equation

**5 =
(3x7) + b**

**5 -
21 = b**

**b =
-16 **(y-intercept)

**____________________**

Our line would cross the y-axis at -16. We have two points (7,5) & (0,-16) and a slope of 3. The slope-intercept form of our line is:

**y =
3x - 16**

We can use the equation we found from the slope/y-intercept form:

**y =
3x - 16**

to help us come up with parametric equations for this line.

First we can set

**x =
t**

then substitute 't' in for 'x' and get the following:

**t =
x**

**y =
3t - 16**

We now have our parametric equations for a line that passes through (7,5) with a slope of 3- see below for the graphical representation (t ranging from -20.. 20):

As the graph shows, this new line crosses the y-axis at -16, passes through (7, 5), and also has a slope = 3.