The question is "Find parametric equations for the line with the given properties:
Slope -2, passing through (-10, -20)."
I don't even know where to begin, or what to do. Please help! This is an example problem, not the main homework problem, I just need to know how to do those kinds of problems.
To find the parametric equations for a line, you need to use the point-slope form of a line equation. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, you are given the slope as -2 and a point on the line as (-10, -20). Now, substitute these values into the point-slope form:
y - (-20) = -2(x - (-10))
Simplify this equation:
y + 20 = -2(x + 10)
Next, we can rewrite this equation in slope-intercept form (y = mx + b) by simplifying further:
y + 20 = -2x - 20
Subtract 20 from both sides:
y = -2x - 40
Now, to express the line in parametric form, we can use the following equations:
x = x1 + at
y = y1 + bt
where (a, b) are any real numbers and (x1, y1) are the coordinates of any point on the line.
Let's choose a = 1 and b = -2 for simplicity. We can use the point (-10, -20) as the initial point.
So, the parametric equations for the line passing through (-10, -20) with a slope of -2 would be:
x = -10 + t
y = -20 - 2t
where t is any real number.
first, look up the definition of Parametric equation. It is a fancy term for something like this:
y=mx+b
m slope is -2, so put in the point (-10,-20) and solve for b
-20=2*(-10)+ b
b=0
y=2x