Find parametric equations for the line of slope 7 that passe

Find parametric equations for the line of slope 7 that passes through the point (2, 5). (Use t as your parametrized variable. Enter your answers as a comma-separated list.)

Solution

We need to recall that the point-slope form looks like the following:

y – y₁ = m(x – x₁)

where m = slope and (x₁, y₁) is the given point

Therefore we can substitute in the given values for the certain variables and solve in the following way.

y – 5 = 7(x – 2)

y – 5 = 7x – 14

y = 7x – 9

So we now have our equation of the line through the point (2, 5) and with a slope of 7 to be y = 7x – 9.

A parametric curve in the plane is a pair of functions

x = f(t)

y = g(t)

Well, we can substitute t in for x.  This would then give us our equation for y in terms of t.

x = t

y = 7t – 9

Therefore, (x , y) = (t , 7t – 9)