Question

MATH (SLOPE Y=MX+B)

WORD PROBLEM (Please answer all questions)

1 In the Heartland area, just south of highway 401, a developer has purchased a parcel of land and would like to build an outdoor go-kart track. The developer wants you to design a track with a simple geometrical shape A) On the grid below, draw a line (x. 5) and a line (y = 1) K-2 B) Draw these two lines on the grid below and determine the slopes of these lines Slope of line x =.5 Answer K-1 Slope of line y = 1 Answer K-1 2. Connect points A (-5, 6) and B (7.1) together. Calculate the slope of the line AB and state the equation of the Line AB in any form (slope and y intercept OR standard form) K-2 B 2 Scale: 2 squares = 1 unit A) The slope of the line AB (show all your work in space below) Answer K-4 B) The equation of the line AB is (use either slope & y-intercept OR standard form) Answer K-3 1 C) Using the grid, you need to find the point of intersection between the two lines (x = -5) and (y = 1) K-2 Answer D) Take the scale given on the grid and determine the height and base of the track by counting the units T-2 Answer (height) Answer (base) T-2 E) Once you have the height and base, find the length of the longest side Answer (longest side) T-4 F) Determine the perimeter of ONLY the track. T.3 Answer (Perimeter-track): G) Next the developer asks you to calculate the area of ONLY the track shape: Answer (Area of triangle) T-4 2

Answer 1

A) X-5 3 2 - (-5,1) y = 1 98 tu 2 3 -3 for x=-5 Slope o=90 i = tano tan so m=co for y=1; X axis es Slope line parallel to tano = tano' mo Slope of line x=-5 i infinite Slope of of line y=1 is

8 A(-5,6) (X2,42) 8(7,1) (x, y) Slope by two points given 7 12-Y x2-x So m= = 5- - 12 -5-7 m = -5 12 Slope of line AB is -5 12 Equation of line y-y2= m(x-2) y-6 = -5 (x+5) (22, Y2) ip 12

line AB r2y- 72 = -5%-25 5x+12y = 47 (c) Point of interfection between two lines is (-5, 1) x = -5 and y=1 height B Bone AC height 2.5 unit 5 cm (2 square + half) square BC base 6 square Assuming 6 unit s 12cm = 2cm square

l A ABC E Longth of longest side : l = AB is a right angled triangle by Pythagoras Theorem (AB)2 = (AC)2 + (CB)2 (AB) = (5) + (12)? (in cm) = 169 25 + 144 A B = √169 AB= 13cm (E) Perimeter of all sides of track sum AB & Bot 5+12+13 AC ㄷ Perimeters 28cm Area = 1, height - X base (@o x 5 x 12 I Area 30 am