Question:Ugh, I hate having to ask because I should know but my book doesn't give enough information. It says
Find the slope of a line that contains the points: (-1,-2) and (-3,-5)
I really am not sure what to do. I can graph it and I know what a slope sorta is. Any help on how to do this would be greatly appreciated.
The slope of a line is the change in Y divided by the change in X.
In your case, the change in Y is -5 - (-2) = -3
and the change in X is -3 - (-1) = -2
The slope is then -3/-2 = 3/2 or 1.5
draw a horizontal line. make dots for -3, -2, -1, and 0.
draw a vertical line perpendicular to the horizontal line. make it intersect where 0 is.
now on the vertical line, make dots for -5, -4, -3, -2, -1, and 0. the 0 of ther vertical line should be the same where the 0 of the horizontal line is.
now make a dot on the bottom left quadrant where -1 (horizontal line) and -2 (vertical line) is.
now make another dot on the bottom left quadrant where -3 (horizontal line) and -5 (vertical line) is.
that is your graph.
for the slope, you just do this:
(-5 - -2) / (-3 - -1) = -3 / -2 = 3 / 2 = 1.5
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say that the coordinates of point 1 are (x_1,y_1) and coordinates of point 2 are (x_2,y_2) then the slope of the line through both points can be found with the following formula:
slope = (y_2 - y_1)/(x_2 - x_1)
This can be seen if you look at the equation of the line:
y = slope*x +k
put in the first point and you get y_1 = slope*x_1 +k
put in the second and you get y_2 = slope*x_2 + k
now subtract the first equation from the second and get:
y_2 - y_1 = slope*(x_2 - x_1)
therefore slope = (y_2 - y_1)/(x_2 - x_1)
Another way to look at this is to recognize that slope tells how many units the line goes up for each unit that it goes to the right. With this knowledge in mind you can draw 2 identically shaped triangles. The first with longside between the points and the second with horizontal side of length 1 and therefore vertical side of length equal the slope. By comparing the triangles and using basic trig you can deduct the same formula.
thats an easy one y2 -y1 over x2-x1. you should get a fraction reduce if you can thats your slope. put that in y=mx+b form and graph starting fromthe far right, you should also start on the y-axis. good luck, i've got to go and do my own homework now.. best of luck to you!! email or better yet, im me if you have any problems or questions.
(-1,-2) and (-3,-5)
(x1, y1) and (x2,y2)