Thread: slope of 1/3

Can a line drawn through (-4,-3) have a slope of 1/3???

any slope you want thru any point in the plane ...

Of course it can. A line drawn through any particular point can have any slope, because those two pieces of information aren't conflicting.

Think about it: if the line passes through (-4,-3), that is its starting point, a piece of information. The slope then tells you in what manner the line "leaves" the point - if the slope is 0, it will be purely horizontal, if the slope is a large number, it will be almost vertical. But no matter what the slope is, the line will always exist, just by spinning it about (-4,-3).

To find the equation of this line, remember that a graph with slope 1/3 will have the following form:

y = (1/3)*x + c

Now solve for c by plugging in the point:

-3 = (1/3)*(-4) + c
c = -3 - (1/3)*(-4) = -5/3

So

y = (x - 5)/3

Double-check that this is correct by plugging in x = -4:

-4 - 5 = -9, then dividing by 3 equals -3, as required.

How can I state the coordinates of two other points on this line?

from (-4,-3) , delta x = 3 , delta y = 1 ... (-1, -2)

do it again from the new point (-1,-2)

I got it already. Thank you. I did a wrong drawing like (-4,0) and (0.-3) and not just (-4.-3). That is why I was so confused, because of the given slope of 1/3. And then it was not possible to draw it with a slope of 1/3.
No everything is clear.