Warm Up F(x) = 3x + 5 find F(2) , F(0), and F(3) +5 Write in your notes. F(x) = 3x + 5 find F(2) , F(0), and F(3) +5 Write the equation of the line in slope intercept form (4,5), (5, 10)

Point Slope Form Y – y1= m (X – x1) You are given ONE point (NOT the intercept) and the SLOPE You will need to fill in what you have to get the equation simplified down to Slope Intercept Form. Y = mX + b

Write the equation of the line given a slope of -3 that passes through (-1,5) Y – y1 = m (X – x1) Plug in the values m = -3 (-1,5) (x1,y1) Y – (5) = (-3) (X- (-1)) Be mindful of the negative Y -5 = -3(X+1) Simplify the Parenthesis Y-5 = -3X -3 Multiply each term by -3 Y = -3X +2 Add 5 to the constant only

Write the equation of a line that has a slope of 2 and passes through (3,8) Y – (8) = (2) (X – 3) Y -8 = 2X and 2*-3 Multiply the slope by each term Y -8 = 2X -6 +8 +8 Add 8 to both sides. Adds to the constant Y = 2X +2 Simplify

Standard Form AX + BY =C A and B are NOT BOTH Zero. A is usually nonnegative AND A,B, and C are real numbers You can interchange between Standard Form, Slope- Intercept Form, and Point-Slope Form.

Write the equation in Standard Form Y + 5 = -5/4 (X -2) Original Equation (Point Slope form) 4(Y +5) = 4 (-5/4) (X-2) Mult. By 4 to get rid of the fraction. 4(Y +5) = -5(X-2) Distribute each side and simplify 4Y +20 = -5X +10 -20 -20 Subtract 20 from each side 4Y = -5X -10 Standard Form has X and Y on the same side. +5X +5X Move X over 5X + 4Y = -10 AX + BY =C Write in Order

Write in Standard Form AX + BY =C Y – 13 = 4 (X -2) Original Equation Y -13 = 4X – 8 Distribute + 13 +13 Add 13 to both sides, simplify Y = 4X + 5 -4X -4X Subtract 4X from both sides, DO NOT combine any terms -4X + Y = 5 -1(-4X + Y) = -1 (5) Multiply by -1 to get “A” positive 4X – Y = -5 Final Answer

Write the equation in Point Slope Form AND Standard Form Point (1,3) m = -2 Y – (3) = -2 (X – (1)) Y -3 = -2 (X -1) Point Slope Form Y -3 = -2X + 2 {-2*-1= 2 change your sign} +3 +3 Y = -2X +5 Slope Intercept Form +2X +2X 2X + Y = 5 Standard Form

Word Problem: Write the example in your notes A home security company provides systems for $5 per week, plus an installation fee. The total fee for 12 weeks of service is $210. Write the Point slope form of an equation to find the total fee Y for any number of X weeks. Write the equation in slope-intercept form What is the flat fee for installation?

A. Point slope form for total fee Y of any number of X weeks Y – y1= m (X – x1) Given information: $5 per week 12 weeks = $210 Slope is rate of change, m= 5 (rate per week) Your point is represented by x and y (x, y) where x is the number of weeks and y is the cost (12, 210) Y – 210 = 5 (X – 12) Plug in given values Point Slope Form

B. Write the equation in Slope Intercept Form Y – 210 = 5(X – 12) Y – 210 = 5X – 60 Distribute +210 +210 Y = 5X + 150 Slope Intercept Form What is the y-intercept on the graph? (0, 150)

C. What is the flat fee for installation? This is another way of asking what is the y- intercept? When your number of weeks equals zero how much will you still pay? Y= 5X + 150 so the flat rate is $150

Classwork. Due at the end of class Pg 290. # 29-51 odd; 72-79 all