Point-Slope Form of a Line: Assignment Flashcards

Point-Slope Form of a Line

• The point-slope form is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line and m denotes the slope.

• For the equation y - 4 = 1/2(x - 1):

  • The slope (m) is 1/2.
  • A specific point on the line is (1, 4).

Finding Point-Slope Equations

• To express a line passing through the point (3, -2) with a slope of -4/5, the equation is y + 2 = -4/5(x - 3).

• A given expression y + 4 = (x + 4) can also be written as y + 4 = 1/2(x + 4) in point-slope format.

Graphing and Identifying Lines

• The function represented by y - 3 = 3/2(x - 4) is depicted correctly by Graph One.

• The linear function derived from the point-slope equation y - 5 = 3(x - 2) is f(x) = 3x - 1.

Analyzing Graphs

• From a graphed linear function, an equation in point-slope form can be written as y + 2 = (1/3)(x + 1) and converted to function notation as f(x) = (1/3)x - (1/3).

• The y-intercept of the graphed linear function is located at the coordinates (0, 4).

Finding Intercepts

• The x-intercept for the equation y + 2 = 2(x + 3) is found to be (-2, 0).

Error Analysis in Function Notation

• In Andy's equation with a slope of 3/4 through the point (3, -2), an error occurs in Step 3:
  • He should have subtracted 2 from both sides instead of adding.

Real-World Applications

• Hugo's payment plan for a bicycle, described by the equation y - 10 = -2(x - 10), indicates that the bicycle costs $30 and will take 15 weeks to pay off if he pays $2 weekly.

• A tile factory's revenue, modeled by y - 3,000 = 0.25(x - 10,000), shows:

  • The revenue function can be expressed as f(x) = 0.25x + 500.
  • A flat delivery fee for the factory is $500, based on a total payment of $3,000 for 10,000 tiles.