Slope/intercept tip

[Jeanette]

This is probably obvious to everyone except me, but if you get a slope/x-y intercept problem, first try to draw the line using the information given. Don't bother trying to solve for x and y. You will quickly be able to see if the slope is positive or negative, steep or shallow, etc. You'll also be able to make a quick estimate of where the intercepts must be.

For example, if the x-intercept equals the y-intercept and x/=/0, just a quick sketch will show you that the slope must be -1. If you're given points, plot the points and take a quick look at which direction the line is pointing.

In PP2 I had two slope questions, and the first one I wasted time trying to solve without plotting, until I realized what an easy question it is when you draw in the line.

[geek_goddess]

There was a PP2 QC question on slopes which I didn't interpret correctly-
The x intercept is twice the y intercept, choose which is bigger, etc -
the slope or 1/2.
I misinterpreted this by taking the modulus rather than taking the values with signs

[Jeanette]

Originally Posted by geek_goddess

There was a PP2 QC question on slopes which I didn't interpret correctly-
The x intercept is twice the y intercept, choose which is bigger, etc -
the slope or 1/2.
I misinterpreted this by taking the modulus rather than taking the values with signs

In this problem, all you need to do is draw a line with the x intercept at 2 and the y at 1, and you see that it has a negative slope so 1/2 is bigger.

[chestnut.cc]

yes thats true... simply drawing out the lines often makes things much simpler... however rem that the rules for negatively sloped lines are exactly the opposite... so a flatter line has a greater slope than a steeper line if theyre both downward sloping... using a 45deg line also helps a lot... giving an idea if the slope is greater than or less than 1...

[DattaPlot54321]

Originally Posted by geek_goddess

There was a PP2 QC question on slopes which I didn't interpret correctly-
The x intercept is twice the y intercept, choose which is bigger, etc -
the slope or 1/2.
I misinterpreted this by taking the modulus rather than taking the values with signs

I actually did this question the other day...I'm pretty sure it was asking if the slope or -1/2 was greater, and I ended up getting that they were equal.

0= ax+b
-b= ax
-b/a = x-intercept

-b/a=2b (x-intercept is twice the y-intercept)

Solve for a:
2ab=-b

a=-b/2b

a=-1/2

That's just how I did it...seemed easier to me than any kind of graphing.

[Goldust]

I agree with DattaPlot. I prefer working with equations. Get any equation of a line in the form of y = mx + c, where m is the slope, c is the y-intercept and -c/m is the x-intercept.

I find this faster than figuring out two points on a graph and then drawing the line.

[Jeanette]

Originally Posted by Goldust

I agree with DattaPlot. I prefer working with equations. Get any equation of a line in the form of y = mx + c, where m is the slope, c is the y-intercept and -c/m is the x-intercept.

I find this faster than figuring out two points on a graph and then drawing the line.

I guess we each need to do what works for us.... If you're given the information that x-intercept=y-intercept, playing around with equations is a waste of time if you just plot, say, (3,0) and (0,3). It's quite easy to see which direction the line is pointing.

[Goldust]

Ah, but if you are given that x-intercept = y-intercept, then you would already know that the slope has to be -1 from the slope formula !

[chestnut.cc]

you can 'see' equations as well i sup...