Comparing graphs of linear relationships with different y-intercepts
About this video
Naomi's savings follow y = 20x + 40: she starts with $40 and saves $20 each month. Her friend Diego also saves $20 a month but starts $60 in debt, so the video graphs his line with the same slope, 20, but starting at -60 on the y-axis.
You'll be able to
- identify the slope and y-intercept of a savings line in context.
- graph a line with the same slope but a different starting value.
- explain that a debt is a negative starting amount.
Key words
- slope
- How much y changes each time x goes up by 1; here, dollars saved per month.
- y-intercept
- The starting value when x = 0; here, savings at month zero.
- debt
- Money you owe, which counts as negative savings.
Transcript
- [Instructor] The graph shows the line y is equal to 20x plus 40, we can see that right over there, which represents Naomi's total savings y after x months. So the savings, that's going to be on the y axis, and then this, the x axis right over here is in months.
Let me label this. This is given in months, months right over here. This is total savings. It's actually labeled. Naomi's friend, Diego, also saves $20 each month, but he starts at $60 in debt. Graph the line that represents Diego's total savings y after x months.
Okay. So let's think about it. It's interesting they say, "Also saves $20 each month." And we could see that that is how much Naomi is saving. Every month that goes by, she is saving an extra $20. And I'm assuming that this right over here is in dollars. That's my tip to draw a sideways dollar sign.
One month goes by, savings goes up by $20. Another month goes by, savings goes up by $20. And we could see that right over here, 20 is indeed the slope. Now, what we see is, is that Naomi started at month zero, started at $40. So the difference between Naomi and Diego is where they're starting.
Diego does not start at $40, he's starting $60 in debt. So we could view that as negative $60 of savings. But from there, he is saving at the exact same rate. Every month that goes by, his savings increases by $20. Every month that goes by, his savings increases by $20.
And so I can get the ruler tool here to actually draw a straight line. Let me see if I can do that. So I'm gonna go from, almost, I'm gonna go from that point to this point and I can now draw the line. So there you have it. I have graphed the line that represents Diego's total savings y after x months.
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