Slopes....I need help.

G

Guest

Guest
Okay there are mostly word problems in this situation which, for me, complicates things a little more.

Here's the problem:

Find the slope of the line(s) that
a. contain (-1,5) and (4,9)
b. 3x-8y=101
c. is parallel to the graph of y=-2/3x + 7.4
d. is perpendicular to the graph of the x=5

Now I know some of the formulas such as (x2-x1/y2-y1) and y=mx+b
but I do not know where to start thinking of how to solve.
 
For this one you need to find the equation of the line.

a. contain (-1,5) and (4,9)

y = mx + b


Use both points to find the gradient.

From -1 to 4 is 5 along the x-axis.

From 5 to 9 is 4 up the y-axis


The gradient is rise/run, y/x, which is


y = ( / )x + b

~~~~~~~~~~~~~~~~~~~~~~~~~

b. 3x-8y=101


Make y the subject.

You could start by adding 8y to both sides.

Then subtract 101 from both sides.

Then divide through by 8.
 
Ok for the first one by the steps....I came out with y=(4/5)+b?
I wouldn't know how to even check my answers to double check if it was right or not.

For the second one...I got a little confused so here's how I worked it out.

3x-8y=101
+8y +8y

3x=101+8y
-101 -101

3x-101=8y



As you can see I have massacred this problem and here's when I get frustrated and remove myself from optimistic thinking.

I don't know how adding 8y to both sides would look nor subtracting the 101.....this is embarrasing...but so will the test paper at the end of next week.
 
Well done.

For a. The gradient is (4/5).

The equation of the line is y = (4/5)x + (29/5), but your not asked for that so do not worry about it.

For b. What you have done is absolutely fine.

Now you just have to divide through by 8 so the y is on its own

Do not be put off by the fact that the answers will be fractions, just put an 8 under both the numbers on the left hand side and remove from the right.

~~~~~~~~~~~~~~~~~~~~~~

Then for this one.

c. is parallel to the graph of y=-2/3x + 7.4

Parallel lines have the same slope!.

~~~~~~~~~~~~~~~~~~~~~~~~~~

For this one

d. is perpendicular to the graph of the x=5

The line in the question is vertical, it's gradient is undefined.

Any horizontal line is perpendicular to it, they have a slope of zero.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(For other lines perpendicular to each the product of their slopes is -1)
 
ok so for b. the slope is 3/8? The equation would be y=3/8x-(12.625) rounded to 13. y=3/8x-13?

I was thinking a number would go where the variables were.

and for a. the slope is 4/5?
 
Yes, well done!

Now that you have done it can you see a short cut for question b?

The last two are more straight forward.


(Hint: 101/8 thats's acceptable and probably preferable,
y = (3/8)x - (101/8))
 
yes indeed thanks.

the whole y over x thing kind of gets you if lose track of the formulas and such.
 
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