Presentation on theme: "5.3 Writing Linear Equations given Two points"— Presentation transcript:
15.3 Writing Linear Equations given Two points Objective Write an equation of a line given twopoints of the line.Steps:Find the slope.y - ym =21x - x21
2Find the y-intercept. Substitute the slope m and the coordinates of one of the points into the slope-intercept form, y = mx + b, and solve for they-intercept b.3. Write an equation of the line. Substitute the slope mand the y-intercept b into the slope-intercept form,y = mx + b.
3EXAMPLEWrite an equation of the line that passes through the points(1, -3) and (3, 5).(x1,y1)(x2,y2)5 – (-3)81. Find the slope.m =m = 4m =3 – 122. Find the y-intercept.Choose one of the ordered pairs.(Either ordered pair will result in the same y-intercept)Using (1, -3)Using (3, 5)y = mx + by = mx + b-3 = 4(1) + b5 = 4(3) + b-3 = 4 + b5 = 12 + b-7 = b-7 = b
4Substitute the slope and the y-intercept into y = mx + b m = and b = -7y = 4x - 7
5EXAMPLEYour Turn1. Find the equation of a line passing through the points(1, 6) and (3, -4).Steps1) Find slope2) Find y-intercept b3) Write equationm = -5b = 11Y = -5x +11
6Two different nonvertical lines are perpendicular if and only if their slopes are opposite reciprocals of each other.Negative Reciprocal ExamplesNumberNegative Reciprocal3-2
7EXAMPLEWrite the equation of a line perpendicular to the liney = -2x + 2 and passing through (6, 8).m = -2.Perpendicular slope = ½.Replace ½ into y =mx +b then find bUse (6,8) for (x,y)8 = ½(6) + b8 = 3 + b5 = bThe equation of the perpendicular line is y = ½ x + 5.
8EXAMPLETry this.Find the equation of a line perpendicular to the equationy = -1/3x – 2 and through the point (-2, -3).m = 3y = mx + b-3 = 3(-2) + b-3 = -6 + b3 = by = 3x + 3
9Objective 22Modeling a real-life situation.A camp program charges a registration fee and a daily amount.If the total bill for one camper was $338 for 12 days and the totalbill for another camper was $506 for 19 days, how much will thebill be for a camper who enrolls for 30 days?Identify the independent variable (x) and the dependentvariable (y).Since part of the bill depends on the number of days, theindependent variable is the number of days.Write the two ordered pairs. (12, 338) and (19, 506)The registration fee is the y-intercept (b). This value is notknow.
10Find the slope and the y-intercept. (12, 338) (19, 506)m =m = 24y = mx + by = 24x + 50This means that the camperpays $24 each day and aregistration fee of $50.338 = 24(12) + b338 = b50 = bIf a camper is there for 30 days, find the cost.y = 24(30) + 50y =y = $770