Lines in the Plane Prerequisite Chapter Section 4.

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Presentation transcript:

Lines in the Plane Prerequisite Chapter Section 4

Slope Ratio of the amount of vertical change to the amount of horizontal change

Slope Find the slope of a line using… 1.A graph “Rise over run” 1.Two ordered pairs formula -

Find the slope of the line through the points (-1, 2) and (4, -2)

Point-Slope Form Equation of a Line Given a point (x 1, y 1 ) and a slope (m), find the equation of the line using f(x) – y 1 = m (x – x 1 )

Find the equation of the line that passes through the point (-3, -4) and has a slope of 2.

Linear Equations Standard Form Ax + By = C Slope-intercept form f(x) = mx + b m = slope b = y-intercept

Definitions Y-intercept: point where a line intersects the y-axis (0, y) X-intercept: point where a line intersects the x-axis (x, 0)

Forms of Equations of Lines General Form Ax + By = C A, B not both 0 Slope-Intercept Form f(x) = m x + b Point-Slope Form f(x) – y 1 = m (x – x 1 ) Vertical Line x = a Horizontal Line f(x) = b

Graphing Linear Equations 2x + 3y = 6 1. Solve equation for y 2. Graph using slope and y-intercept

Slope Parallel lines Their slopes will be EQUAL. Perpendicular lines Their slopes will be the negative reciprocal of each other.

Find an equation of a line through P(1, -2) that is parallel to the line L with equation 3x – 2y = 1

Find an equation of the line through P(2, -3) that is perpendicular to the line L with equation 4x + y = 3.

Camelot Apartments purchased a $50,000 building and depreciates it $2000 per year over a 25-year period. a)Write a linear equation giving the value y of the building in terms of the years x after the purchase. b) In how many years will the value of the building be $24, 500?

Exit Ticket 1. Find the value of x and the value of y for which (x, 14) and (18, y) are points on the graph: y = -2x Find an equation for the line passing through the point and a) parallel to the given line, b) perpendicular to the given line (-2, 3) and y = -2x Bob Michaels purchased a house 8 years ago for $42,000. This year it was appraised at $67,500. a. A linear equation V = mt + b, 0 < t < 15, represents the value of V of the house for 15 years after it was purchased. determine m and b. b.Graph the equation and trace to estimate in how many years after purchase this house will be worth $72,500. c.Write and solve an equation algebraically to determine how many years after purchase this house will be worth $74,000. d.Determine how many years after purchase this house will be worth $80,250.