Slopes yet again!

[kmomma1999]

Can someone help me with finding the slope of this equation?

y=0.15x + 0.79

I thought that the slope was the difference between x1 and x2 and y1 and y2.
Am I wrong?

 

[mmm4444bot]

I thought that the slope was the difference between x1 and x2 and y1 and y2.
Am I wrong?

Hello K Momma:

Yes, what you typed is wrong. (Perhaps, you have the right formula for slope in your head, but you did not type what you are actually thinking.)

The difference between the two y-coordinates (from two known points on a line) AND the difference between the two x-coordinates are both needed to calculate the slope (when the known points are the only information you've got), but these differences are not the slope themselves, as you typed.

What if these two differences turned out to be different numbers? Would that mean there are two different slopes for the same line? No! This is not possible.

The equation that you posted is written in a special form called Slope-Intercept Form.

The reason for this name is that whenever you solve the equation of a line for y, the resulting form displays both the slope and the y-intercept.

Therefore, you do not need to do any calculations to determine the slope of this line. All you need to do is to read the equation while knowing which of the two numbers is the slope and which of the two numbers is the y-intercept.

\(\displaystyle \mbox{Slope} \;=\; \frac{y_2 - y_1}{x_2 - x_1}\)

\(\displaystyle y \;=\; m \cdot x + b\)

This equation is Slope-Intercept Form, where the number m is the slope and the number b is the y-intercept.

The equation that you posted is in this form. Can you see the two numbers in your equation? Is it clear which of these two numbers is the slope?

Make sure to both understand and memorize this basic information.

Cheers,

~ Mark

 

[kmomma1999]

Thank you, yes I do understand it now. Sometimes I do know it but I just cannot concentrate enough to remember that I know it. Thank you very much you have been very helpful!!