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Equations of Lines in the Coordinate Plane

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Equations of Lines in the Coordinate Plane

Section 3.7 p.189

- Definitions:
- Cartesian Coordinate Plane – a graph
- X – axis –
- the horizontal axis of a coordinate plane
- Y – axis –
- the vertical axis of a coordinate plane

- Definitions:
- Origin –
where the two axes meet (0,0)

- Ordered pair –
- x and y values of a point on a graph
- Also called a point of a set of coordinates

- Quadrants – the four sections that the x and y axes divide the coordinate plane into – named I, II, III, and IV

- Identify
- Origin
- Y-axis
- X-axis
- Quadrants I, II, III, and IV

- Slope
- “Steepness”
- What are some examples where slope is a factor?
grade of a road, incline of wheelchair ramp, pitch of a roof, etc.

- Slope
- =
- =
- Pick any two points on a line to compute the slope

- Given A (-1,2) and B (4, -2)
- Find the slope of line AB

- (5, 4) and (3, -1)
- Slope =
- m= =

- Positive vs. negative slope
- Positive slope- rises to the right
- Negative slope- falls to the right

- Horizontal line
- Slope = ∆y = 0 = 0
∆x∆x

- Slope = ∆y = 0 = 0
- Vertical line
- Slope = ∆y = ∆y = undefined
∆x 0

- Slope = ∆y = ∆y = undefined

- Given C (4, 0) and D (4, -2)
- Find the slope of line CD
- undefined

- Special cases:
- x = 4
- What will this slope be?
- y = - 3
- What will this slope be?

- Given
- What is the slope?
- What are the coordinates of the y-intercept?
- (0, -5)

- = )
- Given point A (3, 5) on the line with a slope of -1, find the equation of the line in point-slope form.
- = )
- Write the equation of this line in slope-intercept form.
- =

- What is the equation of a line in point-slope form passing through point A(-2,-1) and B(3, 5)?
- First find the slope;
- Then plug one of the points into the point-slope form of the line;

- What is the equation of a line in slope intercept form with slope of -2 and a y-intercept of (0, 5)?
- In point-slope form?
- y- 5 = -2(x-0)
- What is the equation in point-slope form of the line through (-1, 5) with a slope of 2?
- In slope-intercept form?

- P.194-195 #9-41 odd
- Additional Practice
- 13-2 Slope of a Line worksheet

- How do you think the slopes of parallel lines compare?
- What about perpendicular lines?

- Two non-vertical lines are parallel if and only if their slopes are equal.
- (parallel lines have the same slope)
- Two non-vertical lines are perpendicular if and only if the product of their slopes is -1
- (slopes of perpendicular lines are negative reciprocals of each other)
- m1 *m2 = -1 or m1= -1/m2

- Are the two lines below parallel?
- y= -3x +4 and y=-3x -10
- y= 4x-10 and y=2x-10
- y= x +5 and y = x +7
- Are the two lines below perpendicular?
- y= 4x – 2 and y= -x +5
- y= -x +4 and y= x +4
- y=x -10 and y= +5

- Given a line through points (5,-1) and (-3, 3), find the slope of all lines
- A. parallel to this one
- B. perpendicular to this one

- Slope = (-1 – 3)/ (5 – (-3)) = -4/8 = -1/2
- A. slope = -1/2
- B. slope = 2

- (-4, 2) and (0, -4)
- (-5, -3) and (4, 3)

- p.201-203 #7-10, 15-18, 23, 25, 31, 33
- 13-3 Parallel and Perpendicular Lines worksheet
- 13-7 Writing Linear Equations worksheet #11-23 odd, 24-26 all

A

B

Two points in a horizontal line

Distance = absolute value of the difference in the

x-coordinates

Distance=|-2 – 2| = 4 or |2 – (-2)| = 4

A

B

Two points in a vertical line

Distance = absolute value of the difference in the

y-coordinates

Distance=|-8 – 3| = 11 or |3 – (-8)| = 11

- What about two points that do not lie on a horizontal or vertical line?
- How can you find the distance between the points?
- The distance between two points is equal to the length of the segment with those points as the endpoints

- The distance between points (x1, y1) and (x2, y2) is given by:
- d =
- Find the distance between (0, 0) and (7, 24)
- d =
- d = 25

- Find the midpoint of the line segment with endpoints (4, 7) and (-2, 5)
- (1, 6)

- 13-1 Distance Formula worksheet
- 13-5 Midpoint Formula worksheet