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How Do You Write an Equation of a Line in Slope-Intercept Form from a Word Problem?

Leo's tutoring company profited $1200 after one month of business and $5800 after five months. Assume that his company's profit can be modeled by a straight line. Write an equation in slope-intercept form for the graph of his company's profit over time.

Summary

  1. The '1' in 'x1' and 'y1' means we're talking about our 1st ordered pair
  2. The '2' in 'x2' and 'y2' means we're talking about our 2nd ordered pair
  3. (1,1200) is our 1st point, or ordered pair, on the line, and (5,5800) is our 2nd point
  4. Here, 'm' represents slope, which is the change in 'y' over the change in 'x'
  5. Slope-intercept form is: y=mx+b
  6. Use one of the points to solve for the y-intercept, 'b'
  7. The profit in slope-intercept form is: y=1150x+50
  8. Use the other point to check your answer

Notes

    1. Knowing some x and y-coordinates could help us draw a straight line
    1. Knowing some x and y-coordinates could help us draw a straight line
    2. A pair of x and y-coordinates, also called an ordered pair, means the same as a "point"
    1. 'x' and 'y' are variables found in the equation of a line in slope-intercept form
    2. So any time we're talking about time (in months), that value will be an x-coordinate on our line
    3. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    1. Any time we're talking about time (in months), that value will be an x-coordinate on our line
    2. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    1. Our problem states that after one month, the company profited $1200
    2. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    1. Our problem states that after one month, the company profited $1200
    2. Any time we're talking about time (in months), that value will be an x-coordinate on our line
    3. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    1. Our problem states that after one month, the company profited $1200
    2. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    1. Our problem states that after one month, the company profited $1200
    2. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    3. The '1' in 'y1' just symbolizes that this is the y-coordinate for the first coordinate pair we're looking at on our line
    1. An ordered pair is a pair of x and y-coordinates
    2. '1' is the x-coordinate and '1200' is the y-coordinate in this ordered pair
    1. Any time we're talking about time (in months), that value will be an x-coordinate on our line
    2. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    1. Our problem states that after five months, the company profited $5800
    2. Any time we're talking about time (in months), that value will be an x-coordinate on our line
    3. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    1. Our problem states that after five months, the company profited $5800
    2. Any time we're talking about time (in months), that value will be an x-coordinate on our line
    3. The '2' in 'x2' just symbolizes that this is the x-coordinate for the second coordinate pair we're looking at on our line
    1. Our problem states that after five months, the company profited $5800
    2. Any time a profit is mentioned, we know that value will be a y-coordinate on the line
    3. The '2' in 'y2' just symbolizes that this is the y-coordinate for the second coordinate pair we're looking at on our line
    1. An ordered pair is a pair of x and y-coordinates
    2. '5' is the x-coordinate and '5800' is the y-coordinate in this ordered pair
    1. An ordered pair is a pair of x and y-coordinates
    2. As long as you have at least two points, or ordered pairs, you can draw a straight line!
    1. Our two points are (1,1200) and (5,5800)
    1. Our two points are (1,1200) and (5,5800)
    2. So as you move along a line from one point to another, the change in value of the x-coordinate and y-coordinate is a measure of the line's slope
    1. Our two points are (1,1200) and (5,5800)
    2. So as you move along a line from one point to another, the change in value of the x-coordinate and y-coordinate is a measure of the line's slope
    3. The word 'change' here means the same as 'difference', so we can just subtract the first coordiates from the second coordinates
    4. y2-y1=5800-1200
    5. x2-x1=5-1
    1. Our two points are (1,1200) and (5,5800)
    2. So as you move along a line from one point to another, the change in value of the x-coordinate and y-coordinate is a measure of the line's slope
    3. The word 'change' here means the same as 'difference', so we can just subtract the first coordiates from the second coordinates
    4. y2-y1=5800-1200=4600
    5. x2-x1=5-1=4
    6. The slope is: 4600/4=1150
    1. y2-y1=5800-1200=4600
    2. x2-x1=5-1=4
    3. The slope is: 4600/4=1150
    1. The slope is: 4600/4=1150
    2. Our two points are (1,1200) and (5,5800)
    1. Slope-intercept form is: y=mx+b
    1. Slope-intercept form is: y=mx+b
    2. The 'x' and 'y' can be one of our two ordered pairs, or points
    3. The 'm' is the slope and the 'b' is the y-intercept
    1. Slope-intercept form is: y=mx+b
    2. The 'x' and 'y' can be one of our two ordered pairs, or points
    3. The 'm' is the slope and the 'b' is the y-intercept
    4. m=1150
    1. Slope-intercept form is: y=mx+b
    2. The 'x' and 'y' can be one of our two ordered pairs, or points
    3. The 'm' is the slope and the 'b' is the y-intercept
    4. m=1150
    1. Slope-intercept form is: y=mx+b
    2. The 'x' and 'y' can be one of our two ordered pairs, or points
    3. The 'm' is the slope and the 'b' is the y-intercept
    4. m=1150
    5. So far, our equation in slope-intercept looks like: y=1150x+b
    1. Slope-intercept form is: y=mx+b
    2. The 'x' and 'y' can be one of our two ordered pairs, or points
    3. The 'm' is the slope and the 'b' is the y-intercept
    4. m=1150
    5. So far, our equation in slope-intercept looks like: y=1150x+b
    6. Once we plug in values for 'x' and 'y', we will only have one unknown variable left, 'b', and that's what we need to solve for
    1. So far, our equation in slope-intercept looks like: y=1150x+b
    2. Once we plug in values for 'x' and 'y', we will only have one unknown variable left, 'b', and that's what we need to solve for
    3. Let's plug in '1' for 'x' and '1200' for 'y' in our equation
    1. So far, our equation in slope-intercept looks like: y=1150x+b
    2. Once we plug in values for 'x' and 'y', we will only have one unknown variable left, 'b', and that's what we need to solve for
    3. Plugging in '1' for 'x' and '1200' for 'y' in our equation, we get 1200=1150(1)+b
    1. Our equation looks like this: 1200=1150(1)+b
    2. 1150(1)=1150
    3. 1200-1150=50
    4. 50=b
    1. The y-intercept, 'b', of the company's profit line is '50'
    1. Now we're going to take out the values for 'x' and 'y' in our equation and plug in '50' for 'b'
    2. The y-intercept, 'b', of the company's profit line is '50'
    1. We took out the values for 'x' and 'y' in our equation and plugged in '50' for 'b'
    2. The y-intercept, 'b', of the company's profit line is '50'
    3. '1150' is our slope, 'm'
    4. Slope-intercept form is 'y=mx+b', so we now have an equation for our line in slope-intercept form
    5. Now all you need is either an x-coordinate or a y-coordinate and you can find the other coordinate for that point on the line
    1. The equation for the company's profit is: y=1150x+50
    2. Slope-intercept form is 'y=mx+b', so we now have an equation for our line in slope-intercept form
    3. Now all you need is either an x-coordinate or a y-coordinate and you can find the other coordinate for that point on the line
    1. The equation for the company's profit is: y=1150x+50
    2. We found this equation using one of our two ordered pairs
    3. Since the other ordered pair falls on the same line, we can plug its x and y-coordinates into our new equation to see if we get a true statement
    4. A true statement will tell us that our equation is correct
    1. The equation for the company's profit is: y=1150x+50
    2. We found this equation using one of our two ordered pairs
    3. Since the other ordered pair falls on the same line, we can plug its x and y-coordinates into our new equation to see if we get a true statement
    4. A true statement will tell us that our equation is correct
    1. The equation for the company's profit is: y=1150x+50
    2. We found this equation using one of our two ordered pairs
    3. Since the other ordered pair falls on the same line, we can plug its x and y-coordinates into our new equation to see if we get a true statement
    4. A true statement will tell us that our equation is correct
    1. Our two points are (1,1200) and (5,5800)
    2. Since we found our equation using (1,1200), we can check to make sure it's correct by using (5,5800) since the two points are on the same line
    3. x=5
    4. y=5800
    5. 1150(5)=5750
    6. 5750+50=5800
    1. '5800=5800' is a true statement
    2. A true statement tells that our equation is correct
    1. We found this equation using one of our two ordered pairs
    2. Now all you need is either an x-coordinate or a y-coordinate and you can find the other coordinate for that point on the line