Chapter 4

 Two points determine a line  Standard Form  Ax + By = C  Find the x and the y-intercepts  An equation represents an infinite number of points in a relationships  When given an equation,  make a T-chart  substitute the domain (x values) and find the corresponding range (y- values)

 A point and a slope can name a line  y = mx + b  plot the y-intercept  use the slope to find more points

 Y = 3/4 x – 2  3x + 2y = 6  -2x + 5y = 10  2y = 1

 Increasing  Decreasing  Zero Slope  Undefined Slope or NO slope  y = (positive number)x + b  y = (negative number)x + b  y = constant (domain is all real numbers and the range is the constant)  X = constant (a vertical line is not a function so there is no y-intercept form for it

 Y = x + 7  y = x + 5  Y = x – 1  Y = x – ¾ Change the slope  Y = 1/3x  y = 4x  Y = 10x  Y = -5x  Change both  Y = 1/3x + 7  Y = -3/4x -5  Y = 8x -2  Y = -4x – 3  Y = 5/6x + 9  Change the intercept

WHEN GIVEN A POINT AND A SLOPE (NOT THE Y-INTERCEPT )  Given:  Pt (2,1) and slope 3  Pt((4, -7) and slope - 1  Pt ((2,-3) and slope 1/2 WHEN GIVEN TWO POINTS  Given:  (3,1), (2,4)  (-1, 12), (4, -8)  (5,-8), (-7, 0)

 Given point (3,-2) and slope ¼  Given point (-2, 1) and slope -6  y + 2 = ¼(x – 3)  y –(-2)= ¼(x – 3)  y – 1 = -6(x + 2)  y – 1 = -6(x –(-2))

 y – y 1 = m(x – x 1 ), where (x 1, y 1 ) is a specific point  Where does this equation come from?  m = y 1 – y 2 x 1 – x 2

 Standard Form  Slope- Intercept  Point-Slope  Ax +By = C  y = mx + b  y – y 1 = m(x-x 1 )

 Find the equation in:  Point slope form  Standard form  Slope-intercept form

 You need to know how to identify key elements from each type of equation and when to use each!

 y = 2x – 4  y = -3/4x + 3  y = ½ x – 7  y = -1/2 x + 2  y = -2x + 5  y = -3/4 x  y = -3x + 4  y = 4/3 x – 1  y = 2x + 5  y =.5x - 3

 Parallel lines have the same slope  Write an equation for a line that passes through the point (-3, 5) parallel to the line y = 2x - 4 Write and equation for a line passing through the point (4,-1) and parallel to the line y = ¼ x + 7

 Intersecting lines have different slopes  Write an equation for a line that intersects the line y = -2/3 x + 5 and goes point (-1, 3)  Write an equation for a line that intersects the line 3x – 4y = 10

 The slopes of perpendicular lines are opposite reciprocals  Write and equation for a line that passes through the point (-4,6) and is perpendicular to the line 2x + 3y = 12  Write an equation to a line that passes through the point (4,7) and is perpendicular to the line y = 2/3 x - 1

 Bivariate Data  Regression Lines (line of best fit)  Correlation  Causation  Correlation coefficient (r factor)

 Additive Inverse (opposite)  Multiplicative Inverse (reciprocal)  Square Root (undoes squaring)  Solving Equations

 If one relation contains the element (a,b), then the inverse relation will contain the element (b,a)  EX: A B (-3, -6)(-6, -3) (-1, 4)(4, -1) (2, 9)(9, 2) ((5, -2)(-2, 5) ~Display as a set of ordered pairs, Table, Mapping, Graph

 “Mathalicious example”~ wins per million we reversed to millions per win  y= x + 3  y =2x + 3  y = -1/3x + 2  y = -3/4x -1

 To find the inverse function f-1 (x) of the linear function f(x), complete the following steps:  Step 1~ Replace f(x) with y in the equation f(x)  Step 2~ Interchange y and x in the equation  Step 3~ Solve the equation for y  Step 4~ Replace y with f -1 (x) in the new equation

 f(x) = 4x – 6  f(x) = -1/2x + 11  f(x) = -3x + 9  f(x) = 5/4x – 3  f -1 (x) = x  f -1 (x) = -2x +22  f -1 (x) = -1/3x +3  f -1 (x) = 4/5 x + 12/5

 Mathalicious example”~ wins per million we reversed to millions to win  f(x)=.103x – 2.96 (NFL cost verses wins)  F -1 (x) = 9.7x (NFL wins verses cost)  Celsius verse Fahrenheit  C(x) = 5/9(x – 32  C -1 (x) = F(x) (Fahrenheit)  Car rental cost per day  C(x) = x  C -1 (x) = total number of miles