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Equations of Lines & Applications of Linear Equations in 2 Variables

Equations of Lines & Applications of Linear Equations in 2 Variables. Math 021. The following forms of equations can be used to find the equations of lines given various information: Standard Form : Ax + By = C where A, B, and C are real numbers

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Equations of Lines & Applications of Linear Equations in 2 Variables

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  1. Equations of Lines & Applications of Linear Equations in 2 Variables Math 021

  2. The following forms of equations can be used to find the equations of lines given various information: • Standard Form: Ax + By = C where A, B, and C are real numbers • Slope-Intercept Form: y = mx + b where m is the slope and the y-intercept is (0,b) • Point-Slope Form: y – y1 = m(x – x1) where m is the slope and the point • (x1, y1) is a point on the line.

  3. Examples – Find the equation of each line. Write the answer in standard form: • a. Slope = 3, y-intercept is (0, -2) • b. Slope = -, y-intercept is

  4. Examples – Find the equation of each line. Write the answer in slope-intercept form: • a. Slope = 4, point on line is (1, 3) • b. Slope = -5, point on line is (-6,-1) • c. Slope = , point on line is (4, -3) • d. Slope = - , point on line is (-9,4)

  5. Examples – Find the equation of each line. Write the answer in standard form: • a. Passing through (8, 6) and (9,9) • b. Passing through (-3,4) and (-1,10) • c. Passing through (-8,-6) and (-6,-7)

  6. Examples – Find the equation of each line. Write the answer in standard form: • a. Parallel to y = -3x + 1 passing through (2, 5) • b. Parallel to 8y – 4x = 2 passing through (4, -3) • c. Perpendicular to passing through (-1, 2) • d. Perpendicular to 6y – 3x = -2 passing through (6, -5)

  7. Applications of Linear Equations in 2 Variables • One of applications of linear equations is using the slope of a line to model real world scenarios. The slope of a line is used to represent various rates of change such as: • - Velocity (i.e. miles per hour, meters per second) • - Cost per unit • - Population growth per year

  8. A barrel rolls down a 400 foot incline. After 2 seconds the barrel is rolling 6 ft. per second. After 3 seconds the barrel is rolling at 9 ft. per second. Let t represent the time in seconds, s represent the speed. Assume that the speed of the barrel increases at a linear rate. Use the above information to answer the following: • a. Give two ordered pairs in the form (time, speed) • b. Find an equation in slope-intercept form that represents the relationship between time and speed • c. Use the equation to find the velocity after 5.5 seconds

  9. In 1990, the population of a country was 45,000. In the year 2005, the population of the some country was 60,105. Let x represent years past 1990 and y represent the population. Assume that the population of the country grows at a linear rate. Use the above information to answer the following: • Give two ordered pairs in the form (years past 1990, population) • Find an equation in slope-intercept form that represents the relationship between years after 1990 and population • Use the equation to find the population in the year 1997

  10. A toy company developed a new action figure. After 4 months of being available for purchase, the company sells 52 thousand figures. After 7 months, the company sells 91 thousand figures. Let x represent the number of months of the action figures being available for purchase, let y represent the number of thousands of action figures sold. Assume that the relationship follows a linear pattern. • Give two ordered pairs in the form (months available, thousands of figures sold) • Find an equation in slope-intercept form that represents the relationship between months available for purchase and number of thousands of figures sold • Use the equation to find the number of figures sold 11 months after the action figures are available for purchase.

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