The document discusses point-slope form of linear equations. It provides examples of writing equations in point-slope form given a slope and point, as well as graphing lines from their point-slope form equations. Key aspects include using the difference in y-values as the slope times the difference in x-values, and substituting the point's x- and y-values and given slope into the point-slope form equation y - y1 = m(x - x1).

1. DO NOW 1. From your notes or your memory, write the formula for the slope of a line when you have 2 points. 2. Write down 2 methods we have used to graph a line. 3. y = mx + b. If y = 3x + 1, what is m? What is b? 4. Ax + By = C. If 3x - 4y = 7, what is B? A? C? 5. y - y 1 = m(x - x 1 ). If y - 6 = 3(x - 2), what is x 1 ? y 1 ? m?

2. Agenda Monday, Dec. 6 Do No Homework Check homework 16 p. 307 # 2 - 18 evens Point Slope form 6-4 Ex. 1 & 2

6. Point-Slope Form of Linear Equations Suppose you know that a line passes through the point (3,4) with a slope of 2. You can quickly write an equation of the line using point-slope form. ( y - y 1 ) = m ( x - x 1 ) ( x 1 , y 1 ) is a point on the line and m is the slope. So the difference in y equals the slope times the difference in x. m = ( y - y 1 ) ( x - x 1 )

7. POINT-SLOPE FORM m = y 2 - y 1 x 2 - x 1 y - 5 = ¾ (x - 1 ) Point = (1, 5) Slope = ¾ y - y 1 = m (x - x 1 ) (x 2 - x 1 ) (x 2 - x 1 ) m = y 2 - y 1 x 2 - x 1

8. Graphing Using Point-Slope form Graph the equation ( y - 1) = 2/3( x - 3). The equation shows that the line passes through the point (3, 1) with a slope of 2/3. Start at (3, 1), go up 2 units and right 3 units. Draw your line.

9. Now you try Graph the equation y - 4 = 2( x - 3) Start at (3, 4) go up 2 and right 1.

10. From each equation, name the slope and a point on the line. y - 4 = 3/2 (x - 1 ) 3/2 (1, 4) y - 2 = 3 (x - 5 ) 3 (5, 2) y - 6 = x - 6 1 (6, 6) y + 2 = -3(x + 4) -3 (-4, -2) y - 1 = 1/2(x + 1/2) 1/2 (-1/2, 1) y + 6 = x 1 (0, -6) y - y 1 = m (x - x 1 ) m m m m m m (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 ) (x 1 , y 1 )

11. Write an equation in point-slope form of the line that passes through the point (2, 5) and has a slope of 3. ( y - y 1 ) = m ( x - x 1 ) Substitute the 5 in for y 1 , the 2 in for x 1 and the 3 in for m. y - 5 = 3 ( x - 2 )

12. Now you try: Write the equation of the line with a slope of -3 that passes through the point (-1, 7) in point-slope form. ( y - 7) = -3( x + 1) Write the equation of the line with a slope of 2/3 that passes through the point (10, -8). y + 8 = 2/5(x - 10)

13. Write an equation in point-slope form which goes through the given point(s) with the information given. m = 2 m = -3/2 m = 1/4 m = 1 pt. = (3, 5) pt. = (4, 3) pt. = (-4, -2) pt. = (9, -1) y - 5 = 2(x - 3) y - 3 = -3/2(x - 4) y + 2 = 1/4(x + 4) y + 1 = x - 9 y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 ) y - y 1 = m (x - x 1 )

14. Graph this equation: y - 5 = 1/2 (x - 2) y - y 1 = m (x - x 1 )

15. Graph this equation: y + 3 = 2(x + 1) y - y 1 = m (x - x 1 )

16. Point Slope Form - Things to Remember COPY · It's just a linear equation in a different format. · · When given slope and a point, plug them both in. · · Watch out for negatives. · · When given 2 points, find slope, then use that slope and either point. · · Once you use point-slope, you can change to other forms. y - y 1 = m (x - x 1 )