Lines in the Plane

Prerequisite Chapter

Section 4

SlopeRatio of the amount of vertical

change to the amount of horizontal change

SlopeFind the slope of a line using…1. A graph

“Rise over run”1. Two ordered pairs

formula -12

12

12

12 )()(xxxfxf

xxyym

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

Point-Slope Form Equation of a Line

Given a point (x1, y1) and a slope (m), find the equation of the line using

f(x) – y1 = m (x – x1)

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

Linear EquationsStandard Form

Ax + By = CSlope-intercept form

f(x) = mx + bm = slope

b = y-intercept

DefinitionsY-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 + bPoint-Slope Form f(x) – y1 = m (x – x1)Vertical Line x = aHorizontal Line f(x) = b

Graphing Linear Equations

2x + 3y = 61. Solve equation for y2. Graph using slope and y-intercept

SlopeParallel 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 Ticket1. Find the value of x and the value of y for which (x, 14) and (18, y) are points on the graph: y = -2x + 182.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 + 43.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.