Lada D. answered • 08/23/22
A scientist who likes to teach (online option also available)
So first of all, the slope is not -2/3x but -2/3 because the slope is the bits before the x.
Secondly, you cannot assume that the line goes through the origin. In fact, if you take a graph paper and plot these two points and connect them with a straight line, you will find that it doesn't go close to the origin.
Now if all you are asked to do is graph the line, then plot one of the points and then go a rise of -2 which means down 2 (the negative numbers on the y-axis are downwards, right?) and run of 3 which means to the right 3. So if you had started say with the (-2,3) point, the next point would be (1,1) (down 2 from 3 is 1 and right 3 of -1 is also 1), then it will be ((4,-1). You can also do one more point in that direction. Note these points are going to the lower right corner of the page because a negative slope means the line is left leaning.
What if you wanted more points, this time to the left? Then you reverse both the rise and run directions. So instead of going down 2 you go up 2, but instead of going right 3 you go left 3. From the original (-2,3) point the next point to the left is (-5,5).
Then you connect the dots.
Now to find the y-intercept, you need to get an equation: for a line with slope m and point (x0, y0) the equation is
y-y0=m(x-x0)
In our case the slope m=-2/3 and x0=-2 and y0=3 (you can just as well choose x0=4, y0=-1 since when we finish our work it will give the same answer).
Then the equation for our line is
y-3=-2/3 (x--2)
Remember that --=+ and opening the brackets you should get that
y= -2/3 x+ 5/3
Now you let x=0 to get that y=5/3 ie the y-intercept is (0,5/3). This would be pretty hard to figure out from the graph precisely, but algebra came to the rescue! :)
Paige T.
I knew I was forgetting something. Thank u so much!08/23/22