Question

for a medal!(: Choose the correct slope of the line that passes through the points (−4, 8) and (−3, −6).

7

−14

0

14

Answer 1

You can find the slope between two points \((x_1,y_1), (x_2,y_2)\) with the formula
\[m =\frac{y_2-y_1}{x_2-x_1}\]

Answer 2

still not sure lol

Answer 3

Why not? Plug the numbers into the formula and tell me what you get.

Answer 4

Doesn't matter which point you decide is (x1, y1) and which one is (x2, y2).

Answer 5

-14?

Answer 6

A slope of -14 means a line that when you move +1 point on the x axis, drops 14 points on the y axis. If we go from (-4, 8) to (-3, -6), does it match?

Answer 7

Going from x = -4 to x = -3 is moving +1 point on the x axis.

Answer 8

ughh!!! I'm stuck! is it 14?

Answer 9

A slope of 0 means a line that is horizontal, parallel to the x-axis. That clearly isn't correct here.

Answer 10

Look at those points. What is the y value when x = -4? What is the y value when x = -3?

Answer 11

7!

Answer 12

No, answer my two questions, please...

Answer 13

1. What is the y value when x = -4?

2. What is the y value when x = -3?

Answer 14

-8 and -6?

Answer 15

Close. Take another look. One of those numbers is incorrect.

Answer 16

8*

Answer 17

Right. So as we went from x = -4 to x = -3 (moving +1 on the x-axis), we went from y = 8 to y = -6, which is a move of -14 on the y-axis, right?

Answer 18

yeah

Answer 19

Okay! That means our slope is -14, because for every +1 we move on the x-axis, the y-value changes by -14.

The other two remaining choices can't be right. One of them, 7, means that for every +1 we go on the x-axis, the y-value increases by 7. Well, our y-value decreased, so obviously that isn't correct.

The other choice, -7, means that for every +1 we go on the x-axis, the y-value decreases by 7. Now, that's at least going in the right direction, but it would only take from (-4,8) to (-3,8-7) or (-3, 1). Make sense?

Answer 20

you're right that does make sense! thanks homie

Answer 21

Here's the rule of thumb — if the slope is positive, the line goes up and to the right. Think of it as a graph of your bank balance — a positive slope is a positive thing :-) A negative slope goes down and to the right. The bigger the value of the number, the steeper the slope. A slope of 10 means you go up 10 units for each unit you move along the x axis, whereas a slope of 5 means you go up 5 units, so it isn't as steep. If the slope is between 0 and 1, then you go over more units than you go up. y = x and y = -x make a nice symmetrical x on the piece of graph paper.

Answer 22

okay thanks(:

Answer 23

Final case: a line with no slope! If your equation is x = <some constant>, then you have a vertical line. It doesn't have a slope because all the x-values are the same, so the formula above would divide by 0. You might think of it being the limiting case of an ever steeper slope.

Answer 24

So, armed with this (and some practice) you should be able to look at say

(4,6) and (7,-2) and immediately say "negative slope"

Answer 25

haha okay thanks you were very helpful(:

Answer 26

(-2,3) and (-1,4) positive slope

(-2,3) and (3,4) positive slope, but not steep
(-2,3) and (-1,11) positive slope, steep
etc.

Answer 27

a little time spent practicing will save trouble later :-)

Answer 28

okay thanks doug(: well gtg I'll be on tomorrow maybe you can help me with some more(: