University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

340

Pages:

1
Author:

fynegafn8ps

Mini-Lecture 3.5 Equations of Lines Learning Objectives 1. Use the slope-intercept form to write an equation of a line. 2. Use the slope-intercept form to graph a linear equation. 3. Use the point-slope form to find an equation of a line given its slope and a point on the line. 4. Use the point-slope form to find an equation of a line given two points on the line. 5. Find equations of vertical and horizontal lines. 6. Use the point-slope form to solve problems. Examples: 1. Write an equation of the line with each given slope, m, and y-intercept, (0, b). 2 1 5 31 a) m = -9; b = 4 b) m = − ; b = 7 c) m = 0 ; b = d) m = − ; b = 3 2 2 2 2. Use the slope-intercept form to graph each equation. 1 1 a) y = x − 3 b) y = − x + 2 c) y = −4 x 2 4 d) 5 x + 2 y = 10 3. Find an equation of each line with the given slope that passes through the given point. Write the equation in the form Ax + By = C . a) m = 4; (10, 5) 7 b) m = − ; (5, 2) 9 c) m = −6; (−8, −10) 1 d) m = ; (−4,8) 2 4. Find an equation of the line passing through each pair of points. Write the equation in the form Ax + By = C. a) (-7, -4) and (0, 5) b) (3, 7) and (-2, -6) ⎛ 1 3⎞ ⎛ 5 1⎞ d) ⎜ − , ⎟ and ⎜ − , ⎟ ⎝ 2 4⎠ ⎝ 3 3⎠ c) (9, -9) and (6, -5) 5. Find an equation of each line. a) Vertical line through (0,5) b) Horizontal line through (4,3) 6. Solve. Assume the following describes a linear relationship. Write an equation in slope-intercept form. A faucet is used to add water to a large bottle that already contains some water. After it has been filling for 3 seconds, the gauge on the bottle indicates that it contains 10 ounces of water. After it has been filling for 20 seconds, the gauge indicates the bottle contains 24 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that models the amount of water in the bottle in terms of x. Teaching Notes: • • Many students do not understand that you leave “x and y” in the final equation. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) y=-9x+4; 1b) y = − 2 5 31 x + 7 ; 1c) y = ½; 1d) y = − x + ; 2a)-2d) see mini-lecture graphing 3 2 2 answers; 3a) 4x-y=35; 3b) 7x+9y=53; 3c) 6x+y=-58; 3d) x-2y=-20; 4a) 9x-7y=-35; 4b) 13x-5y=4; 4c) 4x+3y=9; 4d) 5x-14y=-13; 5a) x =0; 5b) y = 3; 6) 14x – 17y = -128