What is the slope of the line? 2-99. In this problem, you will write the equation of the line that goes through the points in the table below.  Use the questions below to help you organize your work. (18,64) (14,52) ∆𝑥=−4 ∆𝑦=−12 𝑚= ∆𝑦 ∆𝑥 = −12 −4 =3 (29,97) (-8,-14) ∆𝑥=−37 ∆𝑦=−111 𝑚= ∆𝑦 ∆𝑥 = −111 −37 =3 y = mx + b (14,52) 52 = 3(14) + b 52 = 42 + b 10 = b No, because they all are on the same line. Check by substituting in a point. What is the slope of the line?  Does it matter which points you use to calculate the slope of the line?  Calculate the slope using two other points to verify your answer to part (a). How can you use a point to write the equation?  Write the equation of the line.  Once you have the slope, does it matter which point you use to write your equation?  Why or why not?  How can you verify that your equation is correct? 

2.3.2 Writing the Equation of a Line Through 2 Points HW: 2-102,103,104,106 September 25, 2018

Objectives CO: SWBAT write the equations of lines from two points on a table or graph. LO: SWBAT construct viable arguments and critique the reasoning of others, model with mathematics, use appropriate tools strategically, and attend to precision.

2-100. LINE FACTORY LOGO The Line Factory needs a new logo for its pamphlet.  After much work, two stylish logos were proposed.  The design department knows the coordinates of the special points in each logo.  However, programmers need to have the equations of the lines to program their pamphlet-production software. Work in pairs today.  Choose one logo for each pair in your team to work on, dividing up the work.  What are the equations of the four line segments that make up this logo?      What are the domain and range of each of the line segments in the logo?  Is the line increasing or decreasing in this interval on the x-axis?    Trade equations with the other pair of students in your team.  Sketch each of their equations on graph paper.  How did each sketch compare with the original logos?  Discuss any equation modifications needed with your team. In pairs

Design A: y = 5x − 7,  increasing D: 35 ≤ x ≤ 57, R: 168 ≤ y ≤ 278 y = 0.5x + 150.5, increasing D: 35 ≤ x ≤79, R: 168≤ y ≤190 y = −0.5x + 229.5, decreasing D: 79 ≤ x ≤ 123, R: 168 ≤ y ≤190 y =168,  neither D: 35 ≤ x ≤ 123, R: y = 168 Design B: y = −2x + 183, decreasing D: 21 ≤ x ≤ 64, R: 55 ≤ y ≤ 141 y = 0.5x + 23, increasing D: 64 ≤ x ≤ 128, R: 55 ≤ y ≤ 87 y = 45, neither D: 89 ≤ x ≤ 130, R: y = 45 y = −7x +668, decreasing D: 86 ≤ x ≤ 95, R: 3 ≤ y ≤ 66