1-Distance and Midpoint
Midpoint Formula
𝑀=(
𝑥1 +𝑥2 𝑦1 +𝑦2
2
,
2
)
Distance Formula
𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Example: Find the midpoint and distance between (-6, 2) and (4, -1).
Try These!
Find the distance and midpoint. Round to the nearest hundredth.
1. (-1, 8) (-7, -3)
2. (0, -5) (4, -9)
2-Slope
Graphs
𝑅𝑖𝑠𝑒
𝑅𝑢𝑛
Slope Formula
𝑦 −𝑦
𝑚 = 𝑥2 −𝑥1
2
1
Examples:
(-5, -1) (6, -3)
Try These!
1.
4. (-1, 7) (-6, 7)
2.
3.
5. (-4, -9) (-8, 5)
3-Equations of Lines
Point-Slope Form
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
Slope-Intercept Form
𝑦 = 𝑚𝑥 + 𝑏
Examples:
7
Point-Slope: m = − 4 (8, -4)
Slope-Intercept: m = 2
Try These!
Write in point-slope form.
1. m = -2 (-8, 4)
2. m = 5 (-3, 1)
Write in slope-intercept form.
3. m = 7 (-2, 9)
4. m = − 4
1
3
3
(-12, -3)
(6, -1)
4-Slopes of Parallel & Perpendicular Lines
Parallel Lines→ same slope
Perpendicular Lines→ slopes are opposite reciprocals (change sign & flip)
Examples:
⃡ are parallel, perpendicular or neither.
Determine if ⃡𝐴𝐵 and 𝐶𝐷
A(5, 7) B(3, 4) C(-1, 6) D(2, 8)
5
y =3 x + 8
y = 5x + 10
y = 4x – 8
2
Try These!
1.
4
y = − 2x – 10
3
2.
⃡ are parallel, perpendicular or neither.
3. Determine if ⃡𝐴𝐵 and 𝐶𝐷
A(-1, 5) B(0, 8) C(-9, -7) D(-11, -13)
4. y = 2x + 7
4
y= x+1
2
5
5. y = x + 4
9
9
y=− x–6
5
5-Equations of Parallel & Perpendicular Lines
1) Get slope from original equation.
2) Plug slope and point into point-slope form.
3) Distribute and solve for y to get into slope-intercept.
Examples:
Write the slope-intercept form of an equation for the line that passes
through (-7, 4) and is parallel to the graph of y = 9x – 5.
Write the slope-intercept form of an equation for the line that passes
through (8, -2) and is perpendicular to the graph of y = -2x + 3.
Try These!
1. Write the slope-intercept form of an equation for the line that passes
1
through (9, -1) and is parallel to the graph of y = 3x – 15.
2. Write the slope-intercept form of an equation for the line that passes
1
through (-4, -3) and is perpendicular to the graph of y = − 2x – 8.
6-Graphing Lines
y = mx + b
1) Plot y-intercept(b) on y-axis
2) Use slope(m) to rise and run
* y = # → horizontal line
* x = # → vertical line
Examples:
1
2
y = 2x – 7
y = − 3x + 4
y=6
Try these!
1
1. y = 3x -2
3. x = 4
2. y = -x + 9
7-Lines and Transversals
Corresponding:
Alternate Interior:
Alternate Exterior:
Same Side Interior:
Examples:
Name the relationship between x and y.
Try These!
Name the relationship between x and y.
1.
2.
4.
5.
3.
8-Parallel Lines and Transversals
Corresponding → CONGRUENT → SET EQUAL
Alternate Interior → CONGRUENT → SET EQUAL
Alternate Exterior → CONGRUENT → SET EQUAL
Same Side Interior → SUPPLEMENTARY → ADD TO 180°
Examples:
Try These!
1.
2.
3.
4.