University:
High School
Course:
High School Mathematics
Academic year:

2021
Views:

410

Pages:

3
Author:

izdupcimatu

1.3 Modeling with Linear Equations A. VOCABULARY & CONCEPTS X-intercept: where the graph crosses the x-axis. y-intercept: where the graph crosses the y-axis. Slope-intercept form: y = mx + b m is slope b is y-intercept Point-slope form: y - y₁ = m(x - x₁) Use when given slope and a point (x₁, y₁) Slope formula: m = (y₂ - y₁) / (x₂ - x₁) = rise / run positive slope negative slope 0 slope Undefined slope Line of best fit: the line that lies as close as possible to all the data points. Correlation coefficient: a number r between -1 and 1 that measures how well a line fits the data. r near 1 → close to points, positive slope r near -1 → close to points, negative slope r near 0 → points do not lie close to any line. B. EXAMPLES Student Journal p.16 #1-4 B. EXAMPLES Student Journal p.16 #1-4 1. Cell Phone Costs Slope m = rise / run = 1 / 10 y = mx + b y = 1/10x + 50 Interpret slope: numerator = y-values (cost) denominator = x-values (# of texts) Every 10 text messages sent costs $1. or 10 cents per text message. 2. Travel Distance y = mx + b Slope m = 360 / 6 = -60 y = -60x + 360 Interpret slope: numerator = y-values (distance) denominator = x-values (time) The travel distance decreases by 60 miles for every hour traveled. 3. Math Homework Grade y = mx + b Slope m = 10 / 10 = 1 y = 1x + b I need to plug in a point on the line and then solve for b. 85 = 1(10) + b 85 = 10 + b -10 -10 75 = b y = x + 75 The math hw grade increases 1% for every completed hw assignment. Can't tell exactly what the y-intercept is! 4. The cost of parking in a parking garage in Chicago is represented by the equation y = 15x + 20 where y is the total cost (in dollars) and x is the time (in hours). The table shows the total cost to park in a parking garage in Denver. Which city's parking garage charges more per hour and by how much more? After how many hours would parking in both cities cost the same? DENVER Hours, x | 2 | 3 | 4 | 5 Cost, y | 43 | 51 | 59 | 67 Slope = change in y / change in x = 8 / 1 If we subtract by 8 we can find the cost for 1 hour and 0 hours y = 8x + 27 COST = 8(hours) + 27 $8 per hour Chicago charges more per hour by $7. Parking in both cities costs the same at 1 hour of parking CHICAGO COST = 15(hours) + 20 hours | 0 | 1 | 2 | 3 | 4 cost | 20 | 35 | 50 | 65 | 80 (0, 20) ← y-intercept $15 per hour (0, 27) ← y-intercept