How to Use the Slope Intercept Form (in Algebra)
Read the problem., Think of the problem in terms of slope-intercept form., Find the slope of the line., Find the y-intercept., Write the equation in slope-intercept form., Test it out.
Step-by-Step Guide
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Step 1: Read the problem.
Before you can move forward, you need to carefully read the problem to understand what is being asked of you.
Read the following problem:
Your bank account increases linearly each week.
If after 20 weeks of work, your bank account is at $560, while after 21 weeks of work it is at $585, find a way to express the relationship between how much money you've earned and how many weeks you've worked in slope-intercept form. -
Step 2: Think of the problem in terms of slope-intercept form.
You should write y = mx + b and know that "m" represents the change and "b" represents a starting point, where the line "intersects" the y-axis.
Notice that the problem states, "Your bank account increases linearly each week," meaning that you are saving the same amount of money each time, which means it will have a smooth slope.
That "smooth," uniformly consistent savings plan makes it linear.
If you don't save the same amount all the time, then it is not linear. , To find the slope, you have to find the rate of change.
If you started with $560 and now have $585 the next week, then you have earned $25 after 1 week of work.
You can figure this out by subtracting $560 from $585. $585-$560 = $25. , To find the y-intercept, or the "b" in y = mx + b, you'll need to find the starting point of the problem (where it intersects the y-axis.
This means you need to know how much money you started with in your account.
If you had $560 after 20 weeks of work, and you know that you earn $25 after every week of work, then you can multiply 20 x 25 to figure out how much money you earned in those 20 weeks. 20 x 25 = 500, which means that you earned $500 in those weeks.
Since you have $560 after 20 weeks and have earned $500, you can figure out how much you started with by subtracting 500 from
560. 560
- 500 =
60.
Therefore, your "b," or your starting point, is
60. , Now that you know the slope, m, is 25, (25 dollars earned per 1 week), and the intercept, b, is 60, you can plug them into the equation: y = mx + b (fill in some of the "blanks" with info) y = 25x + 60 , In this equation, "y" represents the amount of money earned, and "x" represents the amount of weeks you've worked.
Try plugging a different number of weeks into the equation to see how much money you've earned after a certain amount of weeks.
Try two examples:
How much money have you earned after 10 weeks? Plug "10" into the "x" in the equation to find out. y = 25x + 60 = y = 25(10) + 60 = y = 250 + 60 = y =
310.
After 10 weeks, you've made $310.
How many weeks would you have to work to earn 800 dollars? Plug "800" into the "y" variable of the equation to get the "x". y = 25x + 60 = 800 = 25x + 60 = 800
- 60 = 25x = 740 = 25x/25 = 740/25 = x =
29.6.
You can earn 800 dollars in almost 30 weeks. -
Step 3: Find the slope of the line.
-
Step 4: Find the y-intercept.
-
Step 5: Write the equation in slope-intercept form.
-
Step 6: Test it out.
Detailed Guide
Before you can move forward, you need to carefully read the problem to understand what is being asked of you.
Read the following problem:
Your bank account increases linearly each week.
If after 20 weeks of work, your bank account is at $560, while after 21 weeks of work it is at $585, find a way to express the relationship between how much money you've earned and how many weeks you've worked in slope-intercept form.
You should write y = mx + b and know that "m" represents the change and "b" represents a starting point, where the line "intersects" the y-axis.
Notice that the problem states, "Your bank account increases linearly each week," meaning that you are saving the same amount of money each time, which means it will have a smooth slope.
That "smooth," uniformly consistent savings plan makes it linear.
If you don't save the same amount all the time, then it is not linear. , To find the slope, you have to find the rate of change.
If you started with $560 and now have $585 the next week, then you have earned $25 after 1 week of work.
You can figure this out by subtracting $560 from $585. $585-$560 = $25. , To find the y-intercept, or the "b" in y = mx + b, you'll need to find the starting point of the problem (where it intersects the y-axis.
This means you need to know how much money you started with in your account.
If you had $560 after 20 weeks of work, and you know that you earn $25 after every week of work, then you can multiply 20 x 25 to figure out how much money you earned in those 20 weeks. 20 x 25 = 500, which means that you earned $500 in those weeks.
Since you have $560 after 20 weeks and have earned $500, you can figure out how much you started with by subtracting 500 from
560. 560
- 500 =
60.
Therefore, your "b," or your starting point, is
60. , Now that you know the slope, m, is 25, (25 dollars earned per 1 week), and the intercept, b, is 60, you can plug them into the equation: y = mx + b (fill in some of the "blanks" with info) y = 25x + 60 , In this equation, "y" represents the amount of money earned, and "x" represents the amount of weeks you've worked.
Try plugging a different number of weeks into the equation to see how much money you've earned after a certain amount of weeks.
Try two examples:
How much money have you earned after 10 weeks? Plug "10" into the "x" in the equation to find out. y = 25x + 60 = y = 25(10) + 60 = y = 250 + 60 = y =
310.
After 10 weeks, you've made $310.
How many weeks would you have to work to earn 800 dollars? Plug "800" into the "y" variable of the equation to get the "x". y = 25x + 60 = 800 = 25x + 60 = 800
- 60 = 25x = 740 = 25x/25 = 740/25 = x =
29.6.
You can earn 800 dollars in almost 30 weeks.
About the Author
Gloria Martinez
Creates helpful guides on home improvement to inspire and educate readers.
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