MSA mr 1
1) In a linear relationship, as the dependent variable changes at a constant rate, the independent variable goes up at a constant rate too. For example: If John had $100 for his snack money and spent $10 each week, both of the variables will decrease at a steady rate every time John spends $10. The dependent variable would be the number of weeks because the number of weeks depends on how much money you have. The independent variable would be the amount of money, which in this case would be $100 total. If you had a table and graph, you would see that at each week, the amount of money on the y axis would go down $10 at a constant rate.
2) The pattern in a linear relationship shows up in the table, graph, and equation and goes up, down or stays the same at a constant rate. For example, If Jen had $400 and she spent $50 a day, the table would go down at a steady rate on both the x and y axis’s.
(independent)Amount of money left / (dependent)number of days
$400 / 0
$350 / 1
$300 / 2
$250 / 3
$200 / 4
$150 / 5
$100 / 6
$50 / 7
$0 / 8
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From the table, the y axis goes down by $50 at a constant rate each day. On the x axis the number of days go up by 1 at a constant rate each day.
If the pattern is a linear relationship, the graph should go up or down or stay the same at a steady rate and make a straight line, such as the graph below. As the dependent variable changes, the independent variable also goes up, down or stays the same at a constant rate.
1) In a linear relationship, as the dependent variable changes at a constant rate, the independent variable goes up at a constant rate too. For example: If John had $100 for his snack money and spent $10 each week, both of the variables will decrease at a steady rate every time John spends $10. The dependent variable would be the number of weeks because the number of weeks depends on how much money you have. The independent variable would be the amount of money, which in this case would be $100 total. If you had a table and graph, you would see that at each week, the amount of money on the y axis would go down $10 at a constant rate.
2) The pattern in a linear relationship shows up in the table, graph, and equation and goes up, down or stays the same at a constant rate. For example, If Jen had $400 and she spent $50 a day, the table would go down at a steady rate on both the x and y axis’s.
(independent)Amount of money left / (dependent)number of days
$400 / 0
$350 / 1
$300 / 2
$250 / 3
$200 / 4
$150 / 5
$100 / 6
$50 / 7
$0 / 8
________________________________
From the table, the y axis goes down by $50 at a constant rate each day. On the x axis the number of days go up by 1 at a constant rate each day.
If the pattern is a linear relationship, the graph should go up or down or stay the same at a steady rate and make a straight line, such as the graph below. As the dependent variable changes, the independent variable also goes up, down or stays the same at a constant rate.
If you start out with $400 and every day you spend $50, all of the money would be used up by day 8. The variables form a straight line if the pattern is linear.
If you wrote out an equation it would be m=400-(50d) (m= amount of money left, d= number of days). So if you were at 2 days (you replace variable d), you would do : 400- (50 * 2)= m so if you do order of operations you would get $300 left after 2 days. Another example would be if you were at 7 days you would do: 400- (50*7)= m. M would equal $50.
In the table, graph and the equation, the linear relationship can go up, down or stay the same at a constant rate.
If you wrote out an equation it would be m=400-(50d) (m= amount of money left, d= number of days). So if you were at 2 days (you replace variable d), you would do : 400- (50 * 2)= m so if you do order of operations you would get $300 left after 2 days. Another example would be if you were at 7 days you would do: 400- (50*7)= m. M would equal $50.
In the table, graph and the equation, the linear relationship can go up, down or stay the same at a constant rate.
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