1. 6.5 Find an Equation for a Line Given the Slope and a Point We can find the equation of a line from knowing only its SLOPE and a POINT on the line.

2. Find the Equation of a Line Given its Slope and a Point Example #1 (1) Find the equation of a line with a slope of 2 that passes through (2,6) (2) Graph the line

3. Solution Substitute x = 2, y = 6, and m = 2 into the slope y-intercept form of the equation of a line, and solve for b. Substitute x = 2, y = 6, and m = 2 into the slope y-intercept form of the equation of a line, and solve for b. y = mx + b y = mx + b 6 = 2(2) + b 6 = 2(2) + b 6 = 4 + b 6 = 4 + b 6 - 4 =b 6 - 4 =b 2 = b 2 = b Therefore, the y-intercept is 2. Therefore, the y-intercept is 2. The equation of this line is y = 2x + 2 The equation of this line is y = 2x + 2

4. y = 2x + 2

5. Find the Equation of a Partial Variation Tamur knows that it costs $25 to take a taxi to school, which is 10 km from his home. He forgets what the fixed cost is, but remembers that the variable cost is $2/km. Tamur’s friend lives 12 km from his home. Tamur has $60 dollars to spend on the weekend. a) Find the fixed cost and write an equation that relates the cost, in dollars, of a trip to the distance in kilometers. a) Find the fixed cost and write an equation that relates the cost, in dollars, of a trip to the distance in kilometers. b) Find the cost of a 12 km trip. Can Tamur, who has $60 to spend, afford a round trip of this distance? b) Find the cost of a 12 km trip. Can Tamur, who has $60 to spend, afford a round trip of this distance?

6. Solution To find the fixed cost, substitute d = 10, C = 25, and m = 2 into the equation: To find the fixed cost, substitute d = 10, C = 25, and m = 2 into the equation: C = md + b C = md + b 25 = 2(10) + b 25 = 2(10) + b 25 = 20 + b 25 = 20 + b 25 - 20 = b 25 - 20 = b 5 = b 5 = b Therefore, the fixed cost for the taxi fare is $5. Therefore, the fixed cost for the taxi fare is $5. The equation is C = 2d + 5 The equation is C = 2d + 5

7. To find the cost of a 12-km trip, you can substitute d = 12 into the equation To find the cost of a 12-km trip, you can substitute d = 12 into the equation C = 2d + 5 C = 2d + 5 C = 2(12) + 5 C = 2(12) + 5 C = 24 + 5 C = 24 + 5 C = 29 C = 29 Therefore, the total cost of this fare will be $29. Since Tamur has $60, he does have enough money to go there and come back. Therefore, the total cost of this fare will be $29. Since Tamur has $60, he does have enough money to go there and come back.

8. Find the equation of a line that is parallel to x – y – 12 = 0 that passes through (2,-5)

9. Key Information: x – y – 12 = 0 Point on the line: (2, -5) First, rearrange into y= mx + b x – y – 12 = 0 y = x - 12 The slope of this line and a line parallel to it is 1. Substitute m = 1, x = 2, and y = -5 into the equation to solve for b. y = mx + b -5 = 1(2) + b -5 = 2 + b -7 = b Write the equation of the line in y = mx + b form y = x - 7