Question

Find parametric equations for the curve with the given properties.

The line with slope 1/2, passing through (1, -4)

Answer 1

Parametric equations for the line with slope 1/2 passing through the point (1, -4) are x = t + 1 and y = 1/2t - 4, where t is a parameter that can take any real value.

Step-by-step explanation:

To find parametric equations for a line with a given slope that passes through a specific point, we can use the point-slope form of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through. For the line passing through the point (1, -4) with a slope of 1/2, we set up our equation as follows:

y + 4 = 1/2(x - 1)

Now, we introduce a parameter t, such that x = t + 1 and y = 1/2t - 4. This gives us the parametric equations:

x = t + 1

y = 1/2t - 4

Here, t can take any real value, allowing us to trace out the entire line.