Systems with slope

[Audentes]

Am I doing this right?
I need to define m and b for both equations, as well as draw two lines labeled and find the intersection. Then i have to check it.
I started checking it and it doesn’t work.

my new algebra one class is too hard :/

 

[Dr.Peterson]

Am I doing this right?
I need to define m and b for both equations, as well as draw two lines labeled and find the intersection. Then i have to check it.
I started checking it and it doesn’t work.

my new algebra one class is too hard :/

Both graphs are drawn incorrectly. It appears that you are misunderstanding what m and b mean on the graph.

The y-intercept is b; that's the point where the line intersects the y-axis . You put it on the x-axis.

The slope is m; that means how much y increases when x increases by 1; and can be more easily seen when written as a fraction, p/q, as indicating that when x increases by q, y increases by p. You seem to have tried to plot the point (q,p) instead.

Try drawing the graphs again, this time checking that the lines are correct by seeing if a couple points on each line satisfy the equation.

 

[Harry_the_cat]

You've identified m and b correctly for both. Well done!

But both your lines are incorrect.

Let's look at the process:

1. Plot (0, b), the y-intercept. In case 1, that is (0, 4).
2. From that point, interpret the gradient. In case 1, gradient is \(\displaystyle \frac{-1}{1}\). Remember that gradient is \(\displaystyle \frac{rise}{run}\).
So, from (0,4), rise -1 (ie go down 1) and go right 1. That will get you to the point (1, 3). Do it again - that will get you to the point (2, 2).
Join the dots - that's your line.

Try the second one for yourself and show us what you get.

 

[Audentes]

Sorry for the delay, i am taking into consideration all these tips, will get back shortly!
lve had three teachers in algebra one so far this year because of an issue and covid stuff, im trying to catch up on everything in a packet about stuff I didn’t do but this class did.

 

[Audentes]

The y-intercept is b; that's the point where the line intersects the y-axis . You put it on the x-axis.

This helped so much! It seems so simple yet I was missing this.

From that point, interpret the gradient. In case 1, gradient is −11−11\displaystyle \frac{-1}{1}. Remember that gradient is riserunriserun\displaystyle \frac{rise}{run}.
So, from (0,4), rise -1 (ie go down 1) and go right 1. That will get you to the point (1, 3). Do it again - that will get you to the point (2, 2).
Join the dots - that's your line.

perfect, I think this made more sense in my mind.

am i on the right track? I think the line-intersect is at (-3,7), but I still don’t know how to check it and it is frustrating that the lines aren’t perfectly aligned and not exactly on -3 for the x (looks like -3.3)
also: sorry I switched line colors from my previous try to now

 

[Dr.Peterson]

am i on the right track? I think the line-intersect is at (-3,7), but I still don’t know how to check it and it is frustrating that the lines aren’t perfectly aligned and not exactly on -3 for the x (looks like -3.3)
also: sorry I switched line colors from my previous try to now

Your line for y = 2x + 1 has slope -2 instead of 2. You should always check the sign of the slope: a positive slope should be rising from left to right, a negative slope falling.

The check will work better (and the numbers will be more obvious) when you draw it right!

To make sure lines are aligned correctly, I make a series of dots using the slope and put the line through all of them, rather than just make two dots. If you do that, you'll often find that the intersection is exactly on those dots!

 

[Audentes]

Your line for y = 2x + 1 has slope -2 instead of 2. You should always check the sign of the slope: a positive slope should be rising from left to right, a negative slope falling.

The check will work better (and the numbers will be more obvious) when you draw it right!

To make sure lines are aligned correctly, I make a series of dots using the slope and put the line through all of them, rather than just make two dots. If you do that, you'll often find that the intersection is exactly on those dots!

Oh.... I’ll try again, thank you for catching that error.. thanks for the dot advice as well

 

[Audentes]

I got it, thank you! @Dr.Peterson

 

[Dr.Peterson]

Perfect.

And you didn't even need any extra dots, because the second dot on each line happens to be where they meet!