Slopes

[zara-disabled]

Determine Whether the graphs of the pair of lines are perpendicular. Also, look at each original equation, then look at the slope of the line for that equation. You should notice a connection between the numbers. Make a conjecture about what the slope is of a line in the form Ax + By = C. Give the slope in terms of A, B, and/or C. Watch your signs.

2x-5y=-3,
2x+5y=4

Can some one help with this? Can you send it to my e-mail address? zarataz@flash.net.

[TKHunny]

Ax + By = C

The ever-popular "Slope-Intercept" form gives away this information.

y=mx+b

m = the slope

Lines with the same slope are parallel.

Getting from the "Standard Form" to the Slope-Intercept form is a matter of solving for 'y'.

2x-5y=-3 ------ Subtract 2x
-5y= -2x-3 ----- Divide by -5
y=(2/5)x+(3/5) ----- The slope is 2/5

Solving the General Case

Ax+By=C ----- Subtract Ax
By=-Ax+C ----- Divide by B
y=(-A/B)+(C/B) ----- The slope (m) is (-A/B).

Now you solve the last one. Put it in slope-intercept form and simply read the slope. If it is 2/5, the two lines are parallel.

[zara-disabled]

If the slopes are -2/5 and 2/5 are they parallel? How do I graph them to see if they parallel or perpendicular?

Another question:

Find the value of b in 2y = -7x + 3b so that the y-intercept of its graph will be (0,-13)

[TKHunny]

The slopes must be identical for the lines to be parallel. 2/5 and -2/5 doesn't cut it.

For perpendicular, the slope must be the negative reciprocal. 2/5 & -5/2 for example.

How do you graph them? There are many ways. First, tell me if you have StudyWorks and I can shoe you the easiest way. Typically, folks like the slope-intercept form. You can find a point, use the slope to find another, then draw the line.


> Find the value of b in 2y = -7x + 3b so that the y-intercept of its graph will be (0,-13)

Put it in slope-intercept form and solve the piece you you want.

2y = -7x + 3b ------------ Not quite slope-intercept form. - Divide by 2

y = (-7/2)x + (3/2)b --------- That's it. The y-intercept is (3/2)b.

We want (3/2)b = -13 Solve for b...

Just for the record, this is an unfortunate problem. Since the slope-intercept form (y=mx+b) normally uses the parameter 'b', it is kind of confusing to have an unknown quantity named 'b' in the problem. Teachers and authors should choose better names so as to be less confusing. I think.

[ak_smiles-disab]

wow this was an easy explanation . . . thanks alot, it really helped me out too